Information coding in dendritic structures and tags

ABSTRACT

Disclosed are methods and systems that include obtaining at least one image of a dendritic structure, analyzing the at least one image to identify one or more features associated with the dendritic structure, and determining a numerical value associated with the dendritic structure based on the one or more features.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims priority to U.S. Provisional Patent ApplicationNo. 62/076,822, filed on Nov. 7, 2014, the entire contents of which areincorporated herein by reference.

TECHNICAL FIELD

This disclosure relates to dendritic structures, methods for makingdendritic structures, and applications of dendritic structures,including information coding in dendritic structures.

BACKGROUND

The present disclosure relates generally to the formation and use ofdendritic structures. A dendritic structure is a structure that developswith a typical multi-branching, tree-like form. Dendritic patterns arevery common in nature and are illustrated by diverse phenomena such assnowflake formation and lightning. Dendritic crystallization forms anatural fractal pattern. A fractal is generally defined as a rough orfragmented geometric shape that can be subdivided into parts, each ofwhich is (at least stochastically) a reduced-size copy of the whole, aproperty called self-similarity. This self-similarity leads to a finestructure at arbitrarily small scales. Because they appear similar (butnot identical) at all levels of magnification, fractals are oftenconsidered to be infinitely complex. In practice, however, the finestobservable levels of structure will be limited by physical and/orchemical constraints.

SUMMARY

This disclosure features methods for the fabrication of dendriticstructures. In general, a dendritic metal structure can be formed by theelectrodeposition of ions on or in an ion conductor. There are severalviable options for the composition of the ion conductor, which can existas a liquid, solid, or gel. Metals such as silver and copper areparticularly appropriate as they are highly mobile in a variety ofmaterials and are readily reduced and oxidized, which makes theelectrochemical aspects of the process relatively straightforward.

This disclosure also features dendritic structures that are used for awide variety of applications. For example, the dendritic structuresdisclosed herein are used as identification tags for a variety ofcommercial transactions and security applications. Due to their complexnature, dendritic structures are unique and therefore function as“fingerprints,” enabling unique tagging and later identification of awide variety of articles. To permit wide-scale use in commercialenvironments, the disclosure also features methods for implementinglarge-volume fabrication of dendritic structures. Further, thedisclosure features methods and systems for protecting dendriticstructures from tampering once the structures are applied to variousarticles.

Use of dendritic structures for identification and authenticationapplications entails robust analysis and recognition of the structures.Accordingly, the disclosure features methods and systems for acquiringand analyzing images of dendritic structures that rely on the uniqueproperties of the structures to achieve accurate and reproducibleanalysis results.

This disclosure further features methods for storing information in, andreading information from, dendritic structures. For example, thedisclosure features various methods for encoding and/or decodingnumerical values that correspond to morphological features of adendritic structure. By combining multiple features into a scheme,numerical values can be coded in multiple bases, and the range ofpossible coded values is very large.

In general, in a first aspect, the disclosure features methods thatinclude obtaining at least one image of a dendritic tag attached to anarticle, analyzing the at least one image to identify a set of featuresassociated with the dendritic tag, and comparing the set of features tostored information to identify the article.

Embodiments of the methods can include any one or more of the followingfeatures.

The set of features can include a center or origin of a dendriticstructure in the tag. The set of features can include branch points of adendritic structure in the tag. The set of features can include endpoints of branches of a dendritic structure in the tag. The set offeatures comprises a binary grid-based or spatial representation of adendritic structure in the tag.

The stored information can include records stored in a database. Themethods can include transmitting the set of features to a remotecomputing device, and using the remote computing device to perform thecomparison. The methods can include transmitting the at least one imageto a remote computing device, and using the remote computing device toanalyze the at least one image and to perform the comparison.

The methods can include obtaining information about a date ofmanufacture of the article from the stored information. The methods caninclude obtaining information about a place of manufacture of thearticle from the stored information. The methods can include obtaininginformation about transportation of the article from the storedinformation. The information about transportation can includeinformation about handlers of the article at points along a supplychain. The methods can include obtaining information about an expirationdate of the article from the stored information. The methods can includeobtaining information about recall notices for the article from thestored information. The methods can include obtaining health or safetyinformation related to the article from the stored information.

The article can include a food item. The article can include apharmaceutical product. The article can include a medical device.

The methods can include using a mobile telephone to obtain the at leastone image of the dendritic tag. The methods can include authenticatingthe dendritic tag prior to analyzing the at least one image.Authenticating the dendritic tag can include: obtaining a first imageand a second image of the dendritic tag, where the first imagecorresponds to illumination of the tag from a first direction and thesecond image corresponds to illumination of the tag from a seconddirection different from the first direction; and comparing the firstand second images to determine whether a dendritic structure in the taghas a three-dimensional shape. The methods can include determiningwhether the dendritic structure in the tag has a three-dimensional shapebased on patterns of reflected light from the dendritic structure in thefirst and second images. The set of features can include the patterns ofreflected light from the dendritic structure.

Embodiments of the methods can also include any of the other steps orfeatures disclosed herein, including steps or features recited in any ofthe claims, in any combination, as appropriate.

In another aspect, the disclosure features methods that include applyinga dendritic tag to an article or to a container that includes anarticle, obtaining at least one image of the dendritic tag, analyzingthe at least one image to identify a set of features associated with thedendritic tag, and creating a database record that includes informationabout an identity of the article and the set of features associated withthe dendritic tag.

Embodiments of the methods can include any one or more of the followingfeatures.

Applying the dendritic tag can include applying the dendritic tag as aseal over an opening of the container. Applying the dendritic tag caninclude applying the dendritic tag to a product label. Applying thedendritic tag can include applying the dendritic tag over a fastener inthe article or in the container. Applying the dendritic tag can includeapplying the dendritic tag over a seam in the article or in thecontainer. Applying the dendritic tag can include applying the dendritictag over a socket in the article or in the container. Applying thedendritic tag can include applying the dendritic tag to an interior ofthe article or the container, where the dendritic tag is configured todegrade when exposed to light. The dendritic tag can be heat sensitiveso that a dendritic structure in the tag deforms when the tag is heated.

The methods can include obtaining the at least one image using a mobiletelephone.

The article can be a food item. The article can be a pharmaceuticalproduct. The article can be a medical device.

The set of features can include at least one of a center or origin of adendritic structure in the tag, branch points of a dendritic structurein the tag, and end points of branches of a dendritic structure in thetag. The set of features can include a binary grid-based or spatialrepresentation of a dendritic structure in the tag.

The methods can include transmitting the database record to a remotecomputing device that hosts the database. The methods can includetransmitting the set of features to a remote computing device that hoststhe database, and using the remote computing device to create thedatabase record. The methods can include transmitting the at least oneimage to a remote computing device, and using the remote computingdevice to analyze the at least one image and to create the databaserecord.

The methods can include storing additional information about the articlein the database record. The additional information can include a date ofmanufacture of the article. The additional information can include aplace of manufacture of the article. The additional information caninclude information about transportation of the article. The additionalinformation can include an expiration date of the article. Theadditional information can include health or safety information relatedto the article.

The at least one image can include a first image corresponding toillumination of the tag from a first direction, and a second imagecorresponding to illumination of the tag from a second directiondifferent from the first direction. The methods can include storinginformation about patterns of reflected light from a dendritic structurein the tag derived from the first and second images in the databaserecord.

Embodiments of the methods can also include any of the other steps orfeatures disclosed herein, including steps or features recited in any ofthe claims, in any combination, as appropriate.

In a further aspect, the disclosure features methods that includescanning a dendritic tag attached to an article, where the articleincludes an identification card or document, authenticating thedendritic tag based on information derived from the scan, determining aset of features associated with the dendritic tag based on informationderived from the scan, and identifying the article based on the set offeatures.

Embodiments of the methods can include any one or more of the followingfeatures.

Identifying the article can include comparing the set of features tostored information to identify the article. Scanning the dendritic tagcan include obtaining at least two images of the dendritic tag. A firstimage of the at least two images can correspond to illumination of thedendritic tag from a first direction, and a second image of the at leasttwo images can correspond to illumination of the dendritic tag from asecond direction different from the first direction. Scanning thedendritic tag can include scanning the dendritic tag using a capacitivedetector.

The identification card or document can include a passport. Theidentification card or document can include a driver's license. Theidentification card or document can include a security access card.

Authenticating the dendritic tag can include determining whether thedendritic tag includes a three-dimensional dendritic structure. Themethods can include determining whether the dendritic tag includes athree-dimensional dendritic structure based on patterns of reflectedlight from the dendritic structure.

The security access card can be configured for access to a restrictedarea, and the methods can include, following identification of thesecurity access card, transmitting an electronic signal to open therestricted area. The electronic signal can be configured (e.g., caninclude a set of encoded instructions) to open a locked door to therestricted area.

The security access card can be configured for access to a device, andthe methods can include, following identification of the security accesscard, transmitting an electronic signal to grant access to the device.

The security access card can be configured for access to a softwareapplication on a computing device, and the methods can include,following identification of the security access card, transmitting anelectronic signal to grant access to the software application.

The set of features can include at least one of a center or origin of adendritic structure in the tag, branch points of a dendritic structurein the tag, and end points of branches of a dendritic structure in thetag. The set of features can include a binary grid-based or spatialrepresentation of a dendritic structure in the tag.

Identifying the article based on the set of features can includecomparing the set of features to stored information. The storedinformation can include records stored in a database. The methods caninclude transmitting the set of features to a remote computing device,and using the remote computing device to perform the comparison.

The identification card or document can include a security access cardfor accessing secured locations, and the methods can include: obtaininginformation about a location at which the dendritic tag was scanned;obtaining information from the stored information about accesspermissions associated with the security access card at the location;and determining whether the access permissions are sufficient to allowaccess to the location.

The identification card or document can include a security access cardfor accessing secured devices, and scanning the dendritic tag cancorrespond to a request for access to a device. The methods can include:obtaining information from the stored information about accesspermissions associated with the security access card for the device; anddetermining whether the access permissions are sufficient to allowaccess to the device.

The identification card or document can include a security access cardfor accessing software applications, and scanning the dendritic tag cancorrespond to a request for access to a software application. Themethods can include: obtaining information from the stored informationabout access permissions associated with the security access card forthe software application; and determining whether the access permissionsare sufficient to allow access to the software application.

Embodiments of the methods can also include any of the other steps orfeatures disclosed herein, including steps or features recited in any ofthe claims, in any combination, as appropriate.

In another aspect, the disclosure features product identification tagsthat include a dendritic structure featuring at least one metallicmaterial, a substrate supporting the dendritic structure, and aprotective layer that contacts the dendritic structure and the substrateand is positioned to enclose at least a portion of the dendriticstructure.

Embodiments of the tags can include any one or more of the followingfeatures.

The at least one metallic material can include at least one materialselected from the group consisting of silver, copper, zinc, gold, iron,and tin. The protective layer can include at least one material selectedfrom the group consisting of cyanoacrylate, polymethylmethacrylate,polysiloxane, silicon dioxide, and silicon nitride. The protective layercan encapsulate the dendritic structure. The tags can include anadhesive material extending through an aperture in the substrate tocontact the dendritic structure so that when the tag is applied to anarticle, a portion of the dendritic structure is bonded to the articleusing the adhesive material.

The substrate can include a first surface that contacts the dendriticstructure, and a second surface opposite the first surface, where thesecond surface features a plurality of depressions. The depressions cancorrespond to grooves formed in the second surface. The tags can includean adhesive layer that contacts the second surface and features aplurality of extensions that conform to the depressions formed in thesecond surface.

The substrate can include a plurality of cuts extending through at leasta portion of a thickness of the substrate. At least some of theplurality of cuts can extend entirely through the thickness of thesubstrate. At least some of the plurality of cuts can extend through atleast a portion of a thickness of the protective layer.

The tags can include at least one reactive material that reactschemically when exposed to air or water. The at least one reactivematerial can be deposited on portions of the substrate and encapsulatedby the protective layer. The at least one reactive material can includeat least one material selected from the group consisting of acids,oxidizers, and sulfidizing agents. The at least one reactive materialcan be dispersed within the protective layer. The at least one reactivematerial can be contained within one or more blisters encapsulated bythe protective layer. At least one of the one or more blisters can bepositioned between the dendritic structure and the substrate.

The substrate can include at least one material selected from the groupconsisting of polyethylenes, polypropylenes, polyesters, polystyrenes,polyamides, polyolefins, acetates, vinyls, and fluorinated hydrocarbons.The substrate can include paper.

The tags can include an electrolyte layer positioned between thesubstrate and the dendritic structure. The electrolyte layer can includethe at least one metallic material and a solid support material. Theelectrolyte layer can be a gel-based layer featuring the at least onemetallic material. The paper substrate can include ions of the at leastone metallic material. The paper substrate include at least one ofcurrency, a negotiable instrument, an identification document, and acontrolled document.

The tags can include a fluorescent agent attached to the dendriticstructure.

Embodiments of the tags can also include any of the other featuresdisclosed herein, including features recited in any of the claims, inany combination, as appropriate.

In a further aspect, the disclosure features methods for fabricating aproduct identification tag, the methods including applying anelectrolyte material to a substrate material, contacting a surface ofthe substrate material with a plurality of first electrodes, contactingthe electrolyte material with a second electrode, applying an electricalpotential difference between the first plurality of electrodes and thesecond electrode to form a plurality of dendritic structures on thesurface of the substrate material, and applying a protective layer thatcontacts the plurality of dendritic structures and the substrate, andencloses at least a portion of each of the dendritic structures.

Embodiments of the methods can include any one or more of the followingfeatures.

Applying the electrolyte material to the substrate material can includecontacting at least one surface of the substrate material with a bath ofthe electrolyte material. Applying the electrolyte material to thesubstrate can include applying a gel-based electrolyte layer to asurface of the substrate material. Applying the electrolyte material tothe substrate can include immersing the substrate material in a solutionof the electrolyte material. The methods can include drying thesubstrate after formation of the plurality of dendritic structures. Thedendritic structure can include at least one metallic material and theelectrolyte material can include ions of the at least one metallicmaterial.

Each of the plurality of first electrodes can be a cathode, and thesecond electrode can be an anode. The first plurality of electrodes canbe arranged in an array pattern on a common electrode base. Each of thefirst plurality of electrodes can include a tapered tip.

Each of the first plurality of electrodes can be positioned radially ona surface of a roller with a central axis, and contacting the surface ofthe substrate material with the plurality of first electrodes caninclude rotating the roller about its central axis to selectivelycontact the surface with a subset of the plurality of first electrodes.

The second electrode can include a plate. The plate can include aplurality of openings, and the second electrode can be positioned withrespect to the first plurality of electrodes so that each of the firstplurality of electrodes is positioned within a different one of theopenings.

The second electrode can include a plurality of tubes that arepositioned with respect to the first plurality of electrodes so thateach of the first plurality of electrodes is positioned within adifferent one of the tubes. The second electrode can include a pluralityof rings that are positioned with respect to the first plurality ofelectrodes so that each of the first plurality of electrodes ispositioned within a different one of the rings.

The first plurality of electrodes and the second electrode can bepositioned on opposite sides of the substrate material. The firstplurality of electrodes can pierce the substrate material so that thefirst plurality of electrodes extend at least partially through athickness of the substrate material. The first plurality of electrodescan extend fully through the thickness of the substrate material.

The plate can include a fluid conduit connected to at least some of theopenings, and the methods can include applying electrolyte material tothe substrate material by directing the electrolyte material through thefluid conduit and into the at least some of the openings. At least someof the plurality of tubes can include apertures, and the methods caninclude applying electrolyte material to the substrate material byintroducing the electrolyte material into an interior region of the atleast some of the plurality of tubes through the apertures. At leastsome of the plurality of rings can include apertures, and the methodscan include applying electrolyte material to the substrate material byintroducing the electrolyte material into an interior region of the atleast some of the plurality of rings through the apertures.

The methods can include, during formation of the plurality of dendriticstructures, applying an electric field oriented in a directionperpendicular to the surface of the substrate material. A magnitude ofthe electric field can be between 10,000 V/cm and 1,000,000 V/cm.

The methods can include, after formation of the plurality of thedendritic structures and before applying the protective layer, applyingone or more ionized fluorophores to the dendritic structures by applyingan electrical potential to the dendritic structures, and exposing thedendritic structures to the ionized fluorophores during application ofthe electrical potential to attach the fluorophores to the dendriticstructures.

The protective layer can encapsulate at least a portion of each of thedendritic structures. Applying the protective layer can includeenclosing one or more voids in a region between the substrate materialand the protective layer. Applying the protective layer can includedepositing the protective layer in a physical vapor deposition processor a chemical vapor deposition process. Applying the protective layercan include depositing the protective layer as a liquid on the pluralityof dendritic structures. Applying the protective layer can includedepositing the protective layer as a conformal layer over each of theplurality of dendritic structures.

The protective layer can have a Mohs hardness number of 4 or more. Theprotective layer can include at least one material selected from thegroup consisting of polyacrylates, polymethylmethacrylates,polysiloxanes, silicon dioxide, and silicon nitride.

The methods can include, prior to applying the protective layer,depositing at least one reactive material in regions adjacent to theplurality of dendritic structures on the surface of the substratematerial. The methods can include applying the protective layer so thatthe reactive materials are enclosed within the protective layer.

The methods can include separating the substrate material into aplurality of portions, where each portion supports one of the pluralityof dendritic structures. The methods can include bonding at least one ofthe portions to an article using an adhesive material. The at least oneportion can include an opening extending through the portion of thesubstrate material and exposing a region of the dendritic structuresupported by the portion, and the methods can include applying theadhesive material to the exposed region of the dendritic structure sothat the exposed region of the dendritic structure is bonded directly tothe article with the adhesive material.

The methods can include introducing one or more cuts that extend atleast partially through a thickness of the substrate material. Themethods can include introducing one or more cuts that extend completelythrough the thickness of the substrate material and that extendpartially through a thickness of the protective layer.

The methods can include bonding the at least one of the portions to arecess formed in the article. The methods can include contacting atleast one lens to the protective layer. The methods can include formingat least one lens in the protective layer. The methods can includeforming the at least one lens by molding the protective layer on theplurality of dendritic structures and the substrate. The methods caninclude forming the at least one lens by mechanically cutting theprotective layer, or by chemically etching the protective layer.

The methods can include applying one or more fiducial marks to thesubstrate material. Applying the fiducial marks can include exposing theelectrolyte material on the substrate material to spatially patternedillumination light, where the spatial pattern of the illumination lightcorresponds to positions of the fiducial marks.

Embodiments of the methods can also include any of the other steps orfeatures disclosed herein, including steps or features recited in any ofthe claims, in any combination, as appropriate.

In another aspect, the disclosure features dendritic tags that include adendritic structure featuring at least one metallic material, and apaper substrate supporting the dendritic structure.

Embodiments of the tags can include any one or more of the followingfeatures.

The tags can include a protective layer that contacts at least a portionof the dendritic structure, where the protective layer includes at leastone material selected from the group consisting of cyanoacrylate,polymethylmethacrylate, polysiloxane, silicon dioxide, and siliconnitride. The at least one metallic material includes at least onematerial selected from the group consisting of silver, copper, zinc,gold, iron, and tin.

The tags can include an adhesive material extending through an aperturein the substrate to contact the dendritic structure so that when the tagis applied to an article, a portion of the dendritic structure is bondedto the article using the adhesive material.

The paper substrate can include ions of the at least one metallicmaterial. The paper substrate can be formed from a plasticized papermaterial. The paper substrate can be a unit of currency. The papersubstrate can be a negotiable financial instrument. The paper substratecan be a contract. The paper substrate can be an identificationdocument. The paper substrate can be a product label. The papersubstrate can be a controlled document.

Embodiments of the tags can also include any of the other featuresdisclosed herein, including features recited in any of the claims, inany combination, as appropriate.

In a further aspect, the disclosure features methods for fabricating adendritic tag that include applying an electrolyte material to a papersubstrate, contacting a surface of the substrate with an electrode, andapplying an electrical potential to the electrode to form a dendriticstructure on the surface of the substrate.

Embodiments of the methods can include any one or more of the followingfeatures.

Applying the electrolyte material to the paper substrate can includesoaking at least a portion of the paper substrate in the electrolytematerial. The dendritic structure can include at least one metallicmaterial, and the electrolyte material can include ions of the at leastone metallic material. The methods can include drying the papersubstrate following formation of the dendritic structure. The methodscan include applying a protective layer that contacts the dendriticstructure and the paper substrate, and encloses at least a portion ofthe dendritic structure.

The electrode can be a cathode, and the methods can include contacting asurface of the substrate with an anode. The anode can contact thesubstrate at a location that is different from a position opposite tothe cathode. The electrode can be a cathode, and the methods can includecontacting the surface of the substrate with one or more additionalcathodes and applying the electrical potential to each of the cathodesto form a plurality of dendritic structures on the surface of thesubstrate.

Embodiments of the methods can also include any of the other steps orfeatures disclosed herein, including steps or features recited in any ofthe claims, in any combination, as appropriate.

In another aspect, the disclosure features methods that includeobtaining an image of a dendritic structure in a tag attached to anarticle or to a container that includes the article, analyzing the imageto identify a set of features associated with the dendritic structure,where the set of features includes an origin of the dendritic structure,branch points of the dendritic structure, and termination points ofbranches of the dendritic structure, and comparing the set of featuresto reference information for a plurality of dendritic structures todetermine information about the article.

Embodiments of the methods can include any one or more of the followingfeatures.

The comparing can include: (a) selecting a first one of the set offeatures, and identifying reference information corresponding to a firstsubset of the plurality of dendritic structures that include theselected first feature; and (b) selecting a second one of the set offeatures, and identifying reference information corresponding to secondsubset of the plurality of dendritic structures that include theselected second feature, where the second subset is selected from amongthe first subset. The methods can include repeating (b) until theidentified reference information corresponds to a single dendriticstructure from among the plurality of dendritic structures. The methodscan include repeating (b) until the identified reference informationcorresponds to no dendritic structure from among the plurality ofdendritic structures.

Obtaining the image can include illuminating the dendritic structurewith incident light, and measuring reflected light from the dendriticstructure to form the image. The methods can include adjusting at leastone of a contrast and a brightness of the image to highlight edges ofportions of the dendritic structure. The methods can includeconstructing a second image based on the adjusted image by replacingportions of the dendritic structure with line segments. The methods caninclude positioning each of the line segments between correspondingedges of the portions of the dendritic structure. A thickness of eachline segment can be proportional to a distance between the correspondingedges. The methods can include analyzing the second image rather thanthe image formed from measured reflected light to identify the set offeatures.

The methods can include obtaining an additional image of the dendriticstructure, analyzing the additional image to identify a set of featuresassociated with the dendritic structure, where the set of featuresincludes an origin of the dendritic structure, branch points of thedendritic structure, and termination points of branches of the dendriticstructure in the additional image, and comparing the set of featuresderived from the additional image to reference information for theplurality of dendritic structures to determine information about thearticle. The methods can include providing a warning signal if the setof features derived from the additional image does not correspond to asingle dendritic structure from among the plurality of dendriticstructures. The warning signal can include at least one of a visualsignal and an auditory signal.

The methods can include repeating (b) until no change occurs in theidentified reference information. If the identified referenceinformation corresponds to more than one dendritic structure from amongthe plurality of dendritic structures, the methods can includeidentifying a dendritic structure from among the more than one dendriticstructure that corresponds to the dendritic structure in the tag basedon the identified reference information. Identifying a dendriticstructure from among the more than one dendritic structure thatcorresponds to the dendritic structure in the tag based on theidentified reference information can include: for each of the more thanone dendritic structure, extracting information about an article towhich each of the more than one dendritic structure is applied from theidentified reference information; and identifying a dendritic structurefrom among the more than one dendritic structure based on theinformation about the articles to which each of the more than onedendritic structure is applied.

The methods can include obtaining multiple images of the dendriticstructure, where each one of the multiple images is obtained byilluminating the dendritic structure from a different direction anddetecting light reflected from the dendritic structure, analyzing themultiple images to identify patterns of reflected light from thedendritic structure corresponding to each of the different directions,and comparing the patterns of reflected light to the referenceinformation for a plurality of dendritic structures to determine theinformation about the article.

The methods can include obtaining multiple images of the dendriticstructure, where each one of the multiple images can be obtained byilluminating the dendritic structure from a different direction anddetecting light reflected from the dendritic structure. The methods caninclude authenticating the dendritic structure in the tag based oninformation derived from the multiple images. Authenticating thedendritic structure can include determining an authenticity of thedendritic structure based on changes in light reflected from thedendritic structure along the different illumination directions. Themethods can include illuminating the dendritic structure along differentdirections that correspond to fiducial marks on the tag.

The methods can include obtaining the image of the dendritic structureusing a mobile telephone. The methods can include obtaining the image ofthe dendritic structure using an imaging apparatus connected to themobile telephone. The imaging apparatus can include a waveguidepositioned to direct illumination light to the dendritic structure, anda lens positioned to direct reflected light from the dendritic structureto an image sensor of the mobile telephone.

The information about the article can include an identity of thearticle. The methods can include determining whether the article isgenuine based on the identity information. The methods can include: ifthe article is determined to be genuine, providing a first indicator,where the first indicator includes at least one of an audio signal and avisual signal; and if the article is determined to not be genuine,providing a second indicator different from the first indicator, wherethe second indicator includes at least one of an audio signal and avisual signal.

The information about the article can include information about anorigin of the article. The information about the origin of the articlecan include at least one of information about a date of manufacture orharvesting of the article, information about a place of manufacture orharvesting of the article, and information about a manufacturer orharvester of the article. The methods can include determining whetherthe article has reached an expiration date based on the informationabout the origin of the article.

The information about the article can include transit information aboutthe article. The transit information can include information aboutlocations through which the article has passed. The methods can includedetermining whether the article is genuine based on the informationabout locations through which the article has passed.

The information about the article can include security information aboutthe article. The security information can include information aboutaccess permissions to a secure location for a bearer of the article. Themethods can include determining whether to grant access to a securedlocation based on the security information.

The reference information can be stored in a database, and the methodscan include: attaching the tag to the article or to the container thatincludes the article; obtaining an initial image of the dendriticstructure in the tag; analyzing the initial image to identify a set offeatures associated with the dendritic structure, where the set offeatures includes an origin of the dendritic structure, branch points ofthe dendritic structure, and termination points of branches of thedendritic structure; and storing the set of features as the referenceinformation in a database record associated with the article.

The article can include a food product. The article can include apharmaceutical product. The article can include at least one of asecurity access card, a negotiable financial instrument, and anidentification document.

Embodiments of the methods can also include any of the other steps orfeatures disclosed herein, including steps or features recited in any ofthe claims, in any combination, as appropriate.

In a further aspect, the disclosure features methods that includeobtaining an image of a dendritic structure in a tag attached to anarticle or to a container that includes the article, segmenting theimage into a plurality of regions and assigning a binary value to eachregion based on the portion of the dendritic structure in each region,constructing a binary spatial representation of the dendritic structurebased on the plurality of regions, and comparing the binary spatialrepresentation to reference information for a plurality of dendriticstructures to determine information about the article.

Embodiments of the methods can include any one or more of the followingfeatures.

The comparing can include: (a) segmenting the image into a firstplurality of regions, assigning a binary value to each one of the firstplurality of regions, constructing a first binary spatial representationof the dendritic structure based on the first plurality of regions, andidentifying reference information corresponding to a first subset of theplurality of dendritic structures that correspond to the first binaryspatial representation; and (b) segmenting the image into a secondplurality of regions, assigning a binary value to each one of the secondplurality of regions, constructing a second binary spatialrepresentation of the dendritic structure based on the second pluralityof regions, and identifying reference information corresponding to asecond subset of the plurality of dendritic structures that correspondto the second binary spatial representation, where members of the secondplurality of regions are smaller than members of the first plurality ofregions, and wherein the second subset is selected from among the firstsubset. The methods can include repeating (b) until the identifiedreference information corresponds to a single dendritic structure fromamong the plurality of dendritic structures. The methods can includerepeating (b) until the identified reference information corresponds tono dendritic structure from among the plurality of dendritic structures.

The methods can include: obtaining an additional image of the dendriticstructure; segmenting the additional image into a plurality of regions,assigning a binary value to each region in the additional image based onthe portion of the dendritic structure in each region, and constructinga binary spatial representation of the dendritic structure based on theplurality of regions in the additional image; and comparing the binaryspatial representation from the additional image to referenceinformation for a plurality of dendritic structures to determineinformation about the article. The methods can include providing awarning signal if the binary spatial representation derived from theadditional image does not correspond to a single dendritic structurefrom among the plurality of dendritic structures. The warning signal caninclude at least one of a visual signal and an auditory signal.

The methods can include repeating (b) until no change occurs in theidentified reference information. If the identified referenceinformation corresponds to more than one dendritic structure from amongthe plurality of dendritic structures, the methods can includeidentifying a dendritic structure from among the more than one dendriticstructure that corresponds to the dendritic structure in the tag, basedon the identified reference information. Identifying a dendriticstructure from among the more than one dendritic structure thatcorresponds to the dendritic structure in the tag based on theidentified reference information can include: for each of the more thanone dendritic structure, extracting information about an article towhich each of the more than one dendritic structure is applied from theidentified reference information; and

identifying a dendritic structure from among the more than one dendriticstructure based on the information about the articles to which each ofthe more than one dendritic structure is applied.

The methods can include obtaining multiple images of the dendriticstructure, where each one of the multiple images can be obtained byilluminating the dendritic structure from a different direction anddetecting light reflected from the dendritic structure. The methods caninclude authenticating the dendritic structure in the tag based oninformation derived from the multiple images. Authenticating thedendritic structure can include determining an authenticity of thedendritic structure based on changes in light reflected from thedendritic structure along the different illumination directions. Themethods can include illuminating the dendritic structure along differentdirections that correspond to fiducial marks on the tag.

The methods can include obtaining the image of the dendritic structureusing a mobile telephone. The methods can include obtaining the image ofthe dendritic structure using an imaging apparatus connected to themobile telephone. The imaging apparatus can include a waveguidepositioned to direct illumination light to the dendritic structure, anda lens positioned to direct reflected light from the dendritic structureto an image sensor of the mobile telephone.

The information about the article can include an identity of thearticle. The methods can include determining whether the article isgenuine based on the identity information. The methods can include: ifthe article is determined to be genuine, providing a first indicator,where the first indicator includes at least one of an audio signal and avisual signal; and if the article is determined to not be genuine,providing a second indicator different from the first indicator, wherethe second indicator includes at least one of an audio signal and avisual signal.

The information about the article can include information about anorigin of the article. The information about the origin of the articlecan include at least one of information about a date of manufacture orharvesting of the article, information about a place of manufacture orharvesting of the article, and information about a manufacturer orharvester of the article. The methods can include determining whetherthe article has reached an expiration date based on the informationabout the origin of the article.

The information about the article can include transit information aboutthe article. The transit information can include information aboutlocations through which the article has passed. The methods can includedetermining whether the article is genuine based on the informationabout locations through which the article has passed.

The information about the article can include security information aboutthe article. The security information can include information aboutaccess permissions to a secure location for a bearer of the article. Themethods can include determining whether to grant access to a securedlocation based on the security information.

The reference information can be stored in a database, and the methodscan include: attaching the tag to the article or to the container thatincludes the article; obtaining an initial image of the dendriticstructure in the tag; segmenting the initial image into a plurality ofregions and assigning a binary value to each region based on the portionof the dendritic structure in each region of the initial image;constructing a binary spatial representation of the dendritic structurebased on the plurality of regions of the initial image; and storing thebinary spatial representation as the reference information in a databaserecord associated with the article.

The article can include a food product. The article can include apharmaceutical product. The article can include at least one of asecurity access card, a negotiable financial instrument, and anidentification document.

Embodiments of the methods can also include any of the other steps orfeatures disclosed herein, including steps or features recited in any ofthe claims, in any combination, as appropriate.

In another aspect, the disclosure features systems that include anillumination source configured to direct incident light to a dendriticstructure in a tag attached to an article or to a container thatincludes the article, a detector configured to obtain an image bymeasuring incident light reflected from the dendritic structure, and atleast one electronic processor configured to: analyze the image toidentify a set of features associated with the dendritic structure,where the set of features includes an origin of the dendritic structure,branch points of the dendritic structure, and termination points ofbranches of the dendritic structure; and compare the set of features toreference information for a plurality of dendritic structures todetermine information about the article.

Embodiments of the systems can include any one or more of the followingfeatures.

The illumination source and the detector can be enclosed within a commonhousing. The at least one electronic processor can be enclosed withinthe common housing. The at least one electronic processor may not beenclosed within the common housing.

The at least one electronic processor can include a first electronicprocessor enclosed within the common housing and configured to analyzethe image, and a second electronic processor not enclosed within thecommon housing and configured to compare the set of features toreference information. The second electronic processor can be connectedto a computing device that includes a database that includes thereference information.

The illumination source can include a flash unit of a mobile telephone,the detector can include a camera of the mobile telephone, and the atleast one electronic processor can include an electronic processor ofthe mobile telephone. The illumination source can include a flash unitof a mobile telephone, the detector can include a camera of the mobiletelephone, and the first electronic processor can include an electronicprocessor of the mobile telephone. The systems can include an auxiliaryimaging unit connected to the common housing of the mobile telephone andfeaturing a waveguide positioned to direct the incident light to thedendritic structure, and a lens positioned to direct reflected light tothe camera of the mobile telephone.

The at least one electronic processor can be configured to: (a) select afirst one of the set of features, and identify reference informationcorresponding to a first subset of the plurality of dendritic structuresthat include the selected first feature; and (b) select a second one ofthe set of features, and identify reference information corresponding tosecond subset of the plurality of dendritic structures that include theselected second feature, where the second subset is selected from amongthe first subset. The at least one electronic processor can beconfigured to repeat (b) until the identified reference informationcorresponds to a single dendritic structure from among the plurality ofdendritic structures. The at least one electronic processor can beconfigured to repeat (b) until the identified reference informationcorresponds to no dendritic structure from among the plurality ofdendritic structures.

The at least one electronic processor can be configured to adjust atleast one of a contrast and a brightness of the image to highlight edgesof portions of the dendritic structure. The at least one electronicprocessor can be configured to construct a second image based on theadjusted image by replacing portions of the dendritic structure withline segments. The at least one electronic processor can be configuredto position each of the line segments between corresponding edges of theportions of the dendritic structure. The at least one electronicprocessor can be configured to analyze the second image rather than theimage formed from measured reflected light to identify the set offeatures.

The detector can be configured to obtain an additional image of thedendritic structure, and the at least one electronic processor can beconfigured to analyze the additional image to identify a set of featuresassociated with the dendritic structure, where the set of featuresincludes an origin of the dendritic structure, branch points of thedendritic structure, and termination points of branches of the dendriticstructure in the additional image, and compare the set of featuresderived from the additional image to reference information for theplurality of dendritic structures to determine information about thearticle. The at least one electronic processor can be configured toprovide a warning signal if the set of features derived from theadditional image does not correspond to a single dendritic structurefrom among the plurality of dendritic structures. The warning signal caninclude an auditory signal, and the at least one electronic processorcan be configured to activate a sound generator to provide the auditorysignal. The warning signal can include a visual signal, the systems caninclude a display, and the at least one electronic processor can beconfigured to generate the visual signal using the display.

The at least one electronic processor can be configured to repeat (b)until no change occurs in the identified reference information. The atleast one electronic processor can be configured so that if theidentified reference information corresponds to more than one dendriticstructure from among the plurality of dendritic structures, the at leastone electronic processor identifies a dendritic structure from among themore than one dendritic structure that corresponds to the dendriticstructure in the tag based on the identified reference information. Theat least one electronic processor can be configured to identify adendritic structure from among the more than one dendritic structurethat corresponds to the dendritic structure in the tag based on theidentified reference information by: for each of the more than onedendritic structure, extracting information about an article to whicheach of the more than one dendritic structure is applied from theidentified reference information; and identifying a dendritic structurefrom among the more than one dendritic structure based on theinformation about the articles to which each of the more than onedendritic structure is applied.

The detector can be configured to obtain multiple images of thedendritic structure, each one of the multiple images corresponding toillumination of the dendritic structure from a different direction, andthe at least one electronic processor can be configured to analyze themultiple images to identify patterns of reflected light from thedendritic structure corresponding to each of the different illuminationdirections, and compare the patterns of reflected light to the referenceinformation for a plurality of dendritic structures to determine theinformation about the article.

The at least one electronic processor can be configured to authenticatethe dendritic structure in the tag. The detector can be configured toobtain multiple images of the dendritic structure, where each one of themultiple images corresponds to illumination of the dendritic structurewith incident light from the illumination source along a differentdirection, and the at least one electronic processor can be configuredto determine the authenticity of the dendritic structure based onchanges in light reflected from the dendritic structure along thedifferent illumination directions.

The information about the article can include an identity of thearticle. The at least one electronic processor can be configured todetermine whether the article is genuine based on the identityinformation. The at least one electronic processor can be configured sothat: if the article is determined to be genuine, the at least oneelectronic processor provides a first indicator, where the firstindicator includes at least one of an audio signal and a visual signal;and if the article is determined to not be genuine, the at least oneelectronic processor provides a second indicator different from thefirst indicator, where the second indicator includes at least one of anaudio signal and a visual signal.

The information about the article can include information about anorigin of the article. The information about the origin of the articlecan include at least one of information about a date of manufacture orharvesting of the article, information about a place of manufacture orharvesting of the article, and information about a manufacturer orharvester of the article. The at least one electronic processor can beconfigured to determine whether the article has reached an expirationdate based on the information about the origin of the article.

The information about the article can include transit information aboutthe article. The transit information can include information aboutlocations through which the article has passed. The at least oneelectronic processor can be configured to determine whether the articleis genuine based on the information about locations through which thearticle has passed.

The information about the article can include security information aboutthe article. The security information can include information aboutaccess permissions to a secure location for a bearer of the article. Theat least one electronic processor can be configured to determine whetherto grant access to a secured location based on the security information.

The reference information can be stored in a database, the detector canbe configured to obtain an initial image of the dendritic structure inthe tag, and the at least one electronic processor can be configured toanalyze the initial image to identify a set of features associated withthe dendritic structure, where the set of features includes an origin ofthe dendritic structure, branch points of the dendritic structure, andtermination points of branches of the dendritic structure, and store theset of features as the reference information in a database recordassociated with the article.

The article can include a food product. The article can include apharmaceutical product. The article can include at least one of asecurity access card, a negotiable financial instrument, and anidentification document.

Embodiments of the systems can also include any of the other featuresdisclosed herein, including features recited in any of the claims, inany combination, as appropriate.

In a further aspect, the disclosure features systems that include anillumination source configured to direct incident light to a dendriticstructure in a tag attached to an article or to a container thatincludes the article, a detector configured to obtain an image bymeasuring incident light reflected from the dendritic structure, and atleast one electronic processor configured to: segment the image into aplurality of regions and assign a binary value to each region based onthe portion of the dendritic structure in each region; construct abinary spatial representation of the dendritic structure based on theplurality of regions; and compare the binary spatial representation toreference information for a plurality of dendritic structures todetermine information about the article.

Embodiments of the systems can include any one or more of the followingfeatures.

The illumination source and the detector can be enclosed within a commonhousing. The at least one electronic processor can be enclosed withinthe common housing. The at least one electronic processor may not beenclosed within the common housing.

The at least one electronic processor can include a first electronicprocessor enclosed within the common housing and configured to segmentthe image and construct the binary spatial representation, and a secondelectronic processor not enclosed within the common housing andconfigured to compare the binary spatial representation to referenceinformation. The second electronic processor can be connected to acomputing device that includes a database that includes the referenceinformation.

The illumination source can include a flash unit of a mobile telephone,the detector can include a camera of the mobile telephone, and the atleast one electronic processor can include an electronic processor ofthe mobile telephone. The illumination source can include a flash unitof a mobile telephone, the detector can include a camera of the mobiletelephone, and the first electronic processor can include an electronicprocessor of the mobile telephone.

The systems can include an auxiliary imaging unit connected to thecommon housing of the mobile telephone and including a waveguidepositioned to direct the incident light to the dendritic structure, anda lens positioned to direct reflected light to the camera of the mobiletelephone.

The at least one electronic processor can be configured to: (a) segmentthe image into a first plurality of regions, assign a binary value toeach one of the first plurality of regions, construct a first binaryspatial representation of the dendritic structure based on the firstplurality of regions, and identify reference information correspondingto a first subset of the plurality of dendritic structures thatcorrespond to the first binary spatial representation; and (b) segmentthe image into a second plurality of regions, assign a binary value toeach one of the second plurality of regions, construct a second binaryspatial representation of the dendritic structure based on the secondplurality of regions, and identify reference information correspondingto a second subset of the plurality of dendritic structures thatcorrespond to the second binary spatial representation, where members ofthe second plurality of regions are smaller than members of the firstplurality of regions, and where the second subset is selected from amongthe first subset. The at least one electronic processor can beconfigured to repeat (b) until the identified reference informationcorresponds to a single dendritic structure from among the plurality ofdendritic structures. The at least one electronic processor can beconfigured to repeat (b) until the identified reference informationcorresponds to no dendritic structure from among the plurality ofdendritic structures.

The detector can be configured to obtain an additional image of thedendritic structure, and the at least one electronic processor can beconfigured to: segment the additional image into a plurality of regions,assign a binary value to each region in the additional image based onthe portion of the dendritic structure in each region, and construct abinary spatial representation of the dendritic structure based on theplurality of regions in the additional image; and compare the binaryspatial representation from the additional image to referenceinformation for a plurality of dendritic structures to determineinformation about the article. The at least one electronic processor canbe configured to provide a warning signal if the binary spatialrepresentation derived from the additional image does not correspond toa single dendritic structure from among the plurality of dendriticstructures. The warning signal can include an auditory signal, and theat least one electronic processor can be configured to activate a soundgenerator to provide the auditory signal. The warning signal can includea visual signal, the system can include a display, and the at least oneelectronic processor can be configured to generate the visual signalusing the display.

The at least one electronic processor can be configured to repeat (b)until no change occurs in the identified reference information. The atleast one electronic processor can be configured so that if theidentified reference information corresponds to more than one dendriticstructure from among the plurality of dendritic structures, the at leastone electronic processor identifies a dendritic structure from among themore than one dendritic structure that correspond to the dendriticstructure in the tag, based on the identified reference information. Theat least one electronic processor can be configured to identify adendritic structure from among the more than one dendritic structurethat corresponds to the dendritic structure in the tag based on theidentified reference information by: for each of the more than onedendritic structure, extracting information about an article to whicheach of the more than one dendritic structure is applied from theidentified reference information; and identifying a dendritic structurefrom among the more than one dendritic structure based on theinformation about the articles to which each of the more than onedendritic structure is applied.

The detector can be configured to obtain multiple images of thedendritic structure, each one of the multiple images corresponding toillumination of the dendritic structure from a different direction, andthe at least one electronic processor can be configured to analyze themultiple images to identify patterns of reflected light from thedendritic structure corresponding to each of the different illuminationdirections, and compare the patterns of reflected light to the referenceinformation for a plurality of dendritic structures to determine theinformation about the article.

The at least one electronic processor can be configured to authenticatethe dendritic structure in the tag. The detector can be configured toobtain multiple images of the dendritic structure, where each one of themultiple images corresponds to illumination of the dendritic structurewith incident light from the illumination source along a differentdirection, and the at least one electronic processor can be configuredto determine the authenticity of the dendritic structure based onchanges in light reflected from the dendritic structure along thedifferent illumination directions.

The information about the article can include an identity of thearticle. The at least one electronic processor can be configured todetermine whether the article is genuine based on the identityinformation. The at least one electronic processor can be configured sothat: if the article is determined to be genuine, the at least oneelectronic processor provides a first indicator, where the firstindicator includes at least one of an audio signal and a visual signal;and if the article is determined to not be genuine, the at least oneelectronic processor provides a second indicator different from thefirst indicator, where the second indicator includes at least one of anaudio signal and a visual signal.

The information about the article can include information about anorigin of the article. The information about the origin of the articlecan include at least one of information about a date of manufacture orharvesting of the article, information about a place of manufacture orharvesting of the article, and information about a manufacturer orharvester of the article. The at least one electronic processor can beconfigured to determine whether the article has reached an expirationdate based on the information about the origin of the article.

The information about the article can include transit information aboutthe article. The transit information can include information aboutlocations through which the article has passed. The at least oneelectronic processor can be configured to determine whether the articleis genuine based on the information about locations through which thearticle has passed.

The information about the article can include security information aboutthe article. The security information can include information aboutaccess permissions to a secure location for a bearer of the article. Theat least one electronic processor can be configured to determine whetherto grant access to a secured location based on the security information.

The reference information can be stored in a database, the detector canbe configured to obtain an initial image of the dendritic structure inthe tag, and the at least one electronic processor can be configured tosegment the initial image into a plurality of regions and assign abinary value to each region based on the portion of the dendriticstructure in each region of the initial image, construct a binaryspatial representation of the dendritic structure based on the pluralityof regions of the initial image, and store the binary spatialrepresentation as the reference information in a database recordassociated with the article.

The article can include a food product. The article can include apharmaceutical product. The article can include at least one of asecurity access card, a negotiable financial instrument, and anidentification document.

Embodiments of the systems can also include any of the other featuresdisclosed herein, including features recited in any of the claims, inany combination, as appropriate.

In another aspect, the disclosure features methods for generating aunique identifier, the methods including providing a dendriticstructure, reading the dendritic structure to provide a signal, andgenerating a unique identifier from the signal.

Embodiments of the methods can include any one or more of the followingfeatures.

The dendritic structure can include a dendritic metal structure. Thedendritic metal can have an average thickness of no more than about 200nm. The dendritic metal structure can have an average individual segmentwidth of no more than about 100 μm.

The dendritic metal structure can be formed by a method that includesproviding an ion conductor and two or more electrodes in contact withthe ion conductor, and applying a bias voltage across the electrodessufficient to grow the dendritic metal structure in or on the ionconductor extending from the cathode. The ion conductor can be a solid.Alternatively, the ion conductor can be a liquid or gel. The ionconductor can include copper ions or silver ions. The dendritic metalstructure can incorporate the metal of the anode.

At least one of the two or more electrodes and the ion conductor can bein contact with a substrate. The ion conductor can be in contact withthe substrate. Both the anode and the ion conductor can be in contactwith the substrate.

The dendritic structure can be disposed on a substrate. The substratecan include at least one of glass, plastic, metal, paper, fabric,insulator, semiconductor, or a combination thereof. The substrate caninclude a flexible material. A barrier layer can be disposed between thedendritic structure and the substrate.

The dendritic structure can be in contact with an ion conductor duringthe reading of the dendritic structure. The dendritic structure may notbe in contact with an ion conductor during the reading of the dendriticstructure.

Reading the dendritic structure can include optically reading thedendritic structure. Optically reading the dendritic structure caninclude using a camera or array of photodetectors to detect lightreflected from the dendritic structure.

Reading the dendritic structure can include electrically reading thedendritic structure. Electrically reading the dendritic structure caninclude reading the dendritic structure based on its capacitance, themethods including electrically contacting the dendritic structure with aplurality of sensors, and measuring a capacitance at each sensor.Electrically reading the dendritic structure can include reading thedendritic structure based on its resistance, the methods includingelectrically contacting the dendritic structure with a plurality ofsensors, and measuring a resistance at each sensor.

Reading the dendritic structure can include determining x-rayfluorescence information about the dendritic structure. Reading thedendritic structure can include determining reflectance information forthe dendritic structure at radio-frequency wavelengths or measuring anelectromagnetic signal from the dendritic structure at radio-frequencywavelengths. Reading the dendritic structure can include directing radiowaves of different frequencies to the dendritic structure, and detectingat least one of frequencies of radio waves reflected from the dendriticstructure and an electromagnetic response of the dendritic structure.The dendritic structure can be operatively coupled to a radio frequencyantenna or other source of radio frequency waves.

Generating the unique identifier can include applying a numerical methodto the signal provided by the reading of the dendritic structure togenerate the unique identifier. The unique identifier can include atleast one of a number, a binary number, a text string, a set of analogvalues, and an image of the dendritic structure.

The unique identifier can be used to mark an object. The methods caninclude using the unique identifier to track a location of the object.The methods can include destroying the dendritic structure by applying aburst of electrical energy.

Embodiments of the methods can also include any of the other steps orfeatures disclosed herein, including steps or features recited in any ofthe claims, in any combination, as appropriate.

In a further aspect, the disclosure features methods for identifying anobject featuring a dendritic structure, the methods including readingthe dendritic structure to provide a signal, generating a uniqueidentifier from the signal, and identifying the object using the uniqueidentifier.

Embodiments of the methods can include any of the steps or featuresdisclosed herein, including steps or features recited in any of theclaims, in any combination, as appropriate.

In another aspect, the disclosure features methods for authenticating anobject featuring a dendritic structure, the methods including readingthe dendritic structure to provide a signal, generating a uniqueidentifier from the signal, and authenticating the object using theunique identifier.

Embodiments of the methods can include any of the steps or featuresdisclosed herein, including steps or features recited in any of theclaims, in any combination, as appropriate.

In a further aspect, the disclosure features methods for encrypting datausing a dendritic structure, the methods including reading the dendriticstructure to provide a signal, generating a unique identifier from thesignal, and using the unique identifier as a key to encrypt the data.

Embodiments of the methods can include any of the steps or featuresdisclosed herein, including steps or features recited in any of theclaims, in any combination, as appropriate.

In another aspect, the disclosure features methods for accessingencrypted data using a dendritic structure, the methods includingreading the dendritic structure to provide a signal, generating a uniqueidentifier from the signal, and using the unique identifier as a key toaccess the encrypted data.

Embodiments of the methods can include any of the steps or featuresdisclosed herein, including steps or features recited in any of theclaims, in any combination, as appropriate.

In a further aspect, the disclosure features methods that includeobtaining at least one image of a dendritic structure, analyzing the atleast one image to identify one or more features associated with thedendritic structure, and determining a numerical value associated withthe dendritic structure based on the one or more features.

Embodiments of the methods can include any one or more of the followingfeatures.

The one or more features can include one or more angles between segmentsof the dendritic structure. The one or more features can include one ormore lengths of segments of the dendritic structure. The one or morefeatures can include one or more distances of locations on the dendriticstructure from a reference point. The one or more features can includeone or more angles of rotation of locations on the dendritic structurerelative to a reference line.

The analyzing can include, for each of the one or more angles,determining the numerical value by comparing each of the one or moreangles to angular ranges associated with each of the one or more angles.The analyzing can include, for each of the one or more lengths ofsegments, determining the numerical value by comparing each of the oneor more lengths of segments to numerical ranges associated with each ofthe one or more lengths of segments. The analyzing can include, for eachof the one or more distances of locations on the dendritic structure,determining the numerical value by comparing each of the one or moredistances of locations to numerical ranges associated with each of theone or more distances of locations. The analyzing can include, for eachof the one or more angles of rotation of locations on the dendriticstructure, determining the numerical value by comparing each of the oneor more angles of rotation of locations on the dendritic structure toangular ranges associated with each of the one or more angles ofrotation of locations on the dendritic structure.

Determining the numerical value can include determining a binary digitassociated with each of the one or more features. Determining thenumerical value can include determining a base n digit associated witheach of at least some of the one or more features, wherein n is greaterthan 2. The value of n can be 4, or 8, or 16, or can be greater than 16.

The analyzing can include determining a base n digit associated with atleast some of the one or more features by comparing a value of a firstone of the one or more features to at least one range of valuesassociated with the first feature, and comparing a value of a second oneof the one or more features to at least one range of values associatedwith the second feature, where the first and second features are eachselected from the group consisting of an angle between segments of thedendritic structure, a length of a segment of the dendritic structure, adistance of a location on the dendritic structure from a referencepoint, and an angle of rotation of a location on the dendritic structurerelative to a reference line. The value of n can be 4, 8, 16, or greaterthan 16.

The one or more features can include multiple angles between segments ofthe dendritic structure, and the analyzing can include comparing valuesof at least two of the multiple angles to determine the numerical value.The one or more features can include multiple lengths of segments of thedendritic structures, and the analyzing can include comparing values ofat least two of the multiple lengths to determine the numerical value.

The analyzing can include determining a base n digit associated with atleast some of the one or more features by comparing a value of a firstone of the one or more features to a value of a second one of the one ormore features, and comparing a value of a third one of the one or morefeatures to a value of a fourth one of the one or more features. Thevalue of n can be 4, 8, 16, or greater than 16.

The one or more features can include a set of coordinates associatedwith a spatial distribution of the dendritic structure on a coordinatesystem. The coordinate system can be a Cartesian coordinate system. Eachmember of the set of coordinates can correspond to a portion of theCartesian coordinate system, and each portion of the Cartesiancoordinate system can have the same area. The coordinate system can be apolar coordinate system. Each member of the set of coordinates cancorrespond to a sector of the polar coordinate system, and each sectorof the polar coordinate system can have the same area.

The methods can include identifying the set of coordinates bydetermining portions of the coordinate system into which the dendriticstructure extends. The methods can include identifying the set ofcoordinates by determining, for each portion of the coordinate system,whether the dendritic structure extends by more than a threshold amountinto the portion. The threshold amount can be 50%.

The methods can include, prior to identifying the one or more features,determining a fractal dimension associated with at least a portion ofthe dendritic structure, and identifying anomalous features within theat least a portion of the dendritic structure based on the fractaldimension. The methods can include correcting the at least a portion ofthe dendritic structure to remove the anomalous features. Correcting theat least a portion of the dendritic structure can include interpolatingat least one segment of the dendritic structure between points ofdiscontinuity of the dendritic structure.

The methods can include, prior to identifying the one or more features,identifying anomalous segments of the dendritic structure based on agrowth pattern associated with the dendritic structure, and correctingthe dendritic structure by removing the anomalous segments. The methodscan include, prior to identifying the one or more features, analyzingthe dendritic structure to generate a representation of the dendriticstructure that includes a plurality of linear segments, and identifyingthe one or more features from the representation of the dendriticstructure.

The methods can include, prior to obtaining the at least one image ofthe dendritic structure, selecting an information density level at whichthe dendritic structure will be analyzed. Selecting the informationdensity level can correspond to selecting a range of integers, any oneof which the dendritic structure may represent. Selecting theinformation density level can include selecting values associated withone or more of a plurality of analysis attributes. Selecting valuesassociated with one or more of a plurality of analysis attributes caninclude retrieving stored values of the one or more attributes. Themethods can include retrieving the stored values based on informationabout an application of the method. The methods can include determininga security level associated with the application, and retrieving thestored values based on the determined security level.

The plurality of analysis attributes can include a number of readablestates, a number of parameters used, a magnification level, and afractal dimension of the dendritic structure. The plurality of analysisattributes can include a number of image pixels or grid locations usedto analyze the dendritic structure and a fractal dimension of thedendritic structure.

The methods can include selecting a first information density level andanalyzing the dendritic structure at the first information densitylevel, and selecting a second information density level and analyzingthe dendritic structure at the second information density level usinginformation derived from the analysis of the dendritic structure at thefirst information density level. The methods can include adjusting thevalues associated with the one or more analysis attributes to select thesecond information density level. Adjusting the values associated withthe one or more analysis attributes can include retrieving differentstored values of the analysis attributes to select the first and secondinformation density levels. The second information density level can belarger than the first information density level.

The methods can include selecting at least one additional informationdensity level and analyzing the dendritic structure at the at least oneadditional information density level. The at least one additionalinformation density level can be larger than the first and secondinformation density levels.

Embodiments of the methods can also include any of the other steps andfeatures disclosed herein, including steps and features disclosed inconnection with different embodiments and in any of the claims, in anycombination as appropriate.

In another aspect, the disclosure features systems that include adetector configured to obtain at least one image of a dendriticstructure, and an electronic processor configured so that duringoperation of the system, the electronic processor analyzes the at leastone image to identify one or more features associated with the dendriticstructure, and determines a numerical value associated with thedendritic structure based on the one or more features.

Embodiments of the systems can include any one or more of the followingfeatures.

The one or more features can include one or more angles between segmentsof the dendritic structure, one or more lengths of segments of thedendritic structure, one or more distances of locations on the dendriticstructure from a reference point, and/or one or more angles of rotationof locations on the dendritic structure relative to a reference line.

The electronic processor can be configured to analyze the at least oneimage by determining, for each of the one or more angles, the numericalvalue by comparing each of the one or more angles to angular rangesassociated with each of the one or more angles. The electronic processorcan be configured to analyze the at least one image by determining, foreach of the one or more lengths of segments, the numerical value bycomparing each of the one or more lengths of segments to numericalranges associated with each of the one or more lengths of segments. Theelectronic processor can be configured to analyze the at least one imageby determining, for each of the one or more distances of locations onthe dendritic structure, the numerical value by comparing each of theone or more distances of locations to numerical ranges associated witheach of the one or more distances of locations. The electronic processorcan be configured to analyze the at least one image by determining, foreach of the one or more angles of rotation of locations on the dendriticstructure, the numerical value by comparing each of the one or moreangles of rotation of locations on the dendritic structure to angularranges associated with each of the one or more angles of rotation oflocations on the dendritic structure.

The electronic processor can be configured to determine the numericalvalue by determining a binary digit associated with each of the one ormore features. The electronic processor can be configured to determinethe numerical value by determining a base n digit associated with eachof at least some of the one or more features, wherein n is greater than2. The value of n can be 4, 8, 16, or greater than 16.

The electronic processor can be configured to determine a base n digitassociated with at least some of the one or more features by comparing avalue of a first one of the one or more features to at least one rangeof values associated with the first feature, and comparing a value of asecond one of the one or more features to at least one range of valuesassociated with the second feature, where the first and second featuresare each selected from the group consisting of an angle between segmentsof the dendritic structure, a length of a segment of the dendriticstructure, a distance of a location on the dendritic structure from areference point, and an angle of rotation of a location on the dendriticstructure relative to a reference line. The value of n can be 4, 8, 16,or greater than 16.

The one or more features can include multiple angles between segments ofthe dendritic structure, and the electronic processor can be configuredto compare values of at least two of the multiple angles to determinethe numerical value. The one or more features can include multiplelengths of segments of the dendritic structures, and the electronicprocessor can be configured to compare values of at least two of themultiple lengths to determine the numerical value.

The electronic processor can be configured to determine a base n digitassociated with at least some of the one or more features by comparing avalue of a first one of the one or more features to a value of a secondone of the one or more features, and comparing a value of a third one ofthe one or more features to a value of a fourth one of the one or morefeatures. The value of n can be 4, 8, 16, or greater than 16.

The one or more features can include a set of coordinates associatedwith a spatial distribution of the dendritic structure on a coordinatesystem. The coordinate system can be a Cartesian coordinate system. Eachmember of the set of coordinates can correspond to a portion of theCartesian coordinate system, and each portion of the Cartesiancoordinate system can have the same area. The coordinate system can be apolar coordinate system. Each member of the set of coordinates cancorrespond to a sector of the polar coordinate system, and each sectorof the polar coordinate system can have the same area.

The electronic processor can be configured to identify the set ofcoordinates by determining portions of the coordinate system into whichthe dendritic structure extends. The electronic processor can beconfigured to identify the set of coordinates by determining, for eachportion of the coordinate system, whether the dendritic structureextends by more than a threshold amount into the portion. The thresholdamount can be 50%.

Prior to identifying the one or more features, the electronic processorcan be configured to determine a fractal dimension associated with atleast a portion of the dendritic structure, and identify anomalousfeatures within the at least a portion of the dendritic structure basedon the fractal dimension. The electronic processor can be configured tocorrect the at least a portion of the dendritic structure to remove theanomalous features. The electronic processor can be configured tocorrect the at least a portion of the dendritic structure byinterpolating at least one segment of the dendritic structure betweenpoints of discontinuity of the dendritic structure.

Prior to identifying the one or more features, the electronic processorcan be configured to identify anomalous segments of the dendriticstructure based on a growth pattern associated with the dendriticstructure, and correct the dendritic structure by removing the anomaloussegments. Prior to identifying the one or more features, the electronicprocessor can be configured to analyze the dendritic structure togenerate a representation of the dendritic structure that includes aplurality of linear segments, and identify the one or more features fromthe representation of the dendritic structure.

Prior to obtaining the at least one image of the dendritic structure,the electronic processor can be configured to select an informationdensity level at which the dendritic structure will be analyzed. Theelectronic processor can be configured to select the information densitylevel by selecting a range of integers, any one of which the dendriticstructure may represent. The electronic processor can be configured toselect the information density level by selecting values associated withone or more of a plurality of analysis attributes. The electronicprocessor can be configured to select values associated with one or moreof a plurality of analysis attributes by retrieving stored values of theone or more attributes. The electronic processor can be configured toretrieve the stored values based on information about an application ofthe method. The electronic processor can be configured to determine asecurity level associated with the application, and to retrieve thestored values based on the determined security level.

The plurality of analysis attributes can include a number of readablestates, a number of parameters used, a magnification level, and afractal dimension of the dendritic structure. The plurality of analysisattributes can include a number of image pixels or grid locations usedto analyze the dendritic structure and a fractal dimension of thedendritic structure.

The electronic processor can be configured to select a first informationdensity level and analyze the dendritic structure at the firstinformation density level, and select a second information density leveland analyze the dendritic structure at the second information densitylevel using information derived from the analysis of the dendriticstructure at the first information density level. The electronicprocessor can be configured to adjust the values associated with the oneor more analysis attributes to select the second information densitylevel. The electronic processor can be configured to adjust the valuesassociated with the one or more analysis attributes by retrievingdifferent stored values of the analysis attributes to select the firstand second information density levels. The second information densitylevel can be larger than the first information density level.

The electronic processor can be configured to select at least oneadditional information density level and analyze the dendritic structureat the at least one additional information density level. The at leastone additional information density level can be larger than the firstand second information density levels.

Embodiments of the systems can also include any of the other featuresand aspects disclosed herein, including features and aspects disclosedin connection with different embodiments and in any of the claims, inany combination as appropriate.

Certain features, aspects, and steps are disclosed herein in connectionwith particular embodiments. In general, however, those features,aspects, and steps are not particular to those embodiments, and can becombined with other embodiments and other features, aspects, and stepsas desired. Accordingly, while particular embodiments have beendescribed herein for purposes of illustration, it should be appreciatedthat other combinations of the features, aspects, and steps disclosedherein are also within the scope of the disclosure, and that particularembodiments described herein can also include features, aspects, andsteps disclosed in connection with other embodiments.

Unless otherwise defined, all technical and scientific terms used hereinhave the same meaning as commonly understood by one of ordinary skill inthe art to which this disclosure belongs. Although methods and materialssimilar or equivalent to those described herein can be used in thepractice or testing of the subject matter herein, suitable methods andmaterials are described below. All publications, patent applications,patents, and other references mentioned herein are incorporated byreference in their entirety. In case of conflict, the presentspecification, including definitions, will control. In addition, thematerials, methods, and examples are illustrative only and not intendedto be limiting.

The details of one or more embodiments are set forth in the accompanyingdrawings and the description below. Other features and advantages willbe apparent from the description, drawings, and claims.

DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic diagram of a dendritic structure formed on asubstrate.

FIG. 2 is a photomicrograph of a silver dendritic structure formed on anickel cathode.

FIG. 3 is a plot showing a profilometry measurement of a dendriticstructure.

FIG. 4 is a scanning electron micrograph of the edge of a silverdendritic structure on a silver-doped chalcogenide glass.

FIG. 5 is a schematic diagram showing one embodiment of a method forfabricating dendritic structures using a liquid or gel electrolyte.

FIG. 6 is a schematic diagram showing another embodiment of a method forfabricating dendritic structures in which the anode is suspended abovethe surface of the substrate.

FIG. 7 is an image of dendritic metal structures grown between parallelelectrodes.

FIG. 8 is a schematic diagram of an embodiment of an electrical readingapparatus for dendritic structures.

FIG. 9 is a schematic cross-sectional view of an electrical device thatincludes a dendritic metal structure.

FIG. 10A is an image showing an anode and cathode disposed on thesurface of a solar cell.

FIG. 10B is an image showing dendritic structures fabricated on thesurface of the solar cell of FIG. 10A.

FIGS. 11A and 11B are schematic diagrams of a cathode probe array thatis used to fabricate dendritic structures.

FIG. 12 is a schematic diagram of showing penetration of a cathode probearray through a substrate material.

FIG. 13 is a schematic diagram of a cathode probe array that is used tofabricate a linear array of dendritic structures.

FIG. 14 is a schematic diagram of a cathode probe array that is used tofabricate dendritic structures on a continuous substrate.

FIG. 15 is a schematic diagram showing an expanded view of the cathodeprobe array of FIG. 14.

FIG. 16A is a schematic diagram showing a patterned anode that is usedto fabricate dendritic structures.

FIG. 16B is a schematic diagram showing a plurality of anode tubes thatare used to fabricate dendritic structures.

FIG. 16C is a schematic diagram of a plate anode that is used tofabricate dendritic structures.

FIG. 16D is a schematic diagram of an anode that includes a plurality offluid delivery channels.

FIG. 17 is a schematic diagram showing a station for post-processingfabricated dendritic structures.

FIG. 18 is an image of a dendritic structure.

FIG. 19 is a schematic diagram of a dendritic tag with a protectivelayer.

FIG. 20 is a schematic diagram of a dendritic tag with a non-conformalprotective layer.

FIGS. 21A-21C are micrographs of dendritic structures grown on asubstrate with an overlying liquid electrolyte.

FIGS. 22A-22B are micrographs of dendritic structures grown on a solidelectrolyte material.

FIG. 23 is a schematic diagram of a dendritic tag bonded to an articleusing a layer of adhesive.

FIG. 24 is a schematic diagram of a dendritic tag bonded to an articleand having a substrate surface patterned with a series of grooves.

FIG. 25 is a schematic diagram of a dendritic tag that includes aplurality of cuts.

FIG. 26 is a schematic diagram of a dendritic tag bonded to a recessformed in an article.

FIG. 27 is a schematic diagram of a dendritic tag that includesencapsulated reactive materials.

FIG. 28 is a flow chart that shows a series of steps for identifying andauthenticating goods using dendritic tags.

FIG. 29 is a schematic diagram of a scanning device for scanning atagged article and determining tag information.

FIG. 30 is a schematic diagram of a detachable imaging module connectedto a mobile telephone.

FIG. 31A is a schematic diagram of a dendritic tag applied to an articleand featuring an integrally formed lens.

FIG. 31B is a schematic diagram of a dendritic tag applied to an articleand featuring a lens applied to the tag.

FIGS. 32A-32C are schematic diagrams of radial, parallel, and multipledendritic structures, respectively.

FIGS. 33A-33B are scanning electron micrographs of dendritic structureswith tree-like and terrain-like fractal structure in the perpendiculardirection, respectively.

FIGS. 34A-34B are electron micrographs of dendritic structures grown ondifferent solid electrolytes.

FIG. 35 is a flow chart showing a series of steps for identifying anarticle tagged with a dendritic tag.

FIG. 36 is an image of a United States quarter illuminated with ambientfluorescent light and the flash unit of a mobile telephone.

FIG. 37A is a contrast-adjusted image of a dendritic structure.

FIG. 37B is an image of the dendritic structure of FIG. 37A, withidentified features of the dendritic structure overlaid on the image.

FIG. 37C is a schematic diagram showing features identified for thedendritic structure of FIG. 37A.

FIG. 38A an image of a dendritic structure that is used to train analgorithm for dendritic structure feature recognition.

FIG. 38B is an image of a dendritic structure, with features of thestructure identified by a trained algorithm overlaid on the image.

FIG. 39 is a schematic diagram of a cathode with a plurality ofconducting tracks that are connected to a subset of the cathode'sprobes.

FIG. 40 is a schematic diagram of a substrate that includes a pluralityof raised structures and dendritic structures grown on the raisedstructures.

FIG. 41 is a schematic diagram of a dendritic tag applied to a productlabel.

FIG. 42 is a schematic diagram of a dendritic tag applied to a containerof a pharmaceutical product.

FIG. 43 is a schematic diagram of a dendritic tag applied to a containerseal.

FIG. 44A is an image of a dendritic structure formed of silver that wasgrown on a paper substrate.

FIG. 44B is an image of the dendritic structure of FIG. 44A underperpendicular illumination in an optical microscope.

FIG. 44C is an image corresponding to an enlarged portion of the imagein FIG. 44B.

FIGS. 45A-45D are images showing reflected light from the dendriticstructure of FIG. 44B, illuminated from different directions.

FIGS. 46A-46D are contrast-adjusted images that correspond to the imagesof FIGS. 45A-45D, respectively.

FIG. 47A is an image of reflected light from a dendritic structureilluminated from a direction corresponding to the top of the image.

FIG. 47B corresponds to the image of FIG. 47A adjusted for contrast andbrightness to reduce scattered light contributions to the image.

FIG. 47C is an image of reflected light from the dendritic structure ofFIG. 47A, illuminated from a direction corresponding to the left side ofthe image.

FIG. 47D corresponds to the image of FIG. 47C adjusted for contrast andbrightness to reduce scattered light contributions to the image.

FIGS. 48A-48C are schematic diagrams of a line, a square, and a cube,respectively.

FIGS. 49A-49C are schematic diagrams showing first, second, and highergenerational curves formed by replication of the Koch curve.

FIG. 50 is a schematic diagram showing the first, second, and thirdgenerations of the Vicsek fractal.

FIG. 51 is a schematic diagram showing two fractal elements that encodebinary values.

FIGS. 52A and 52B are plots of information units and capacity,respectively, against magnification for the Koch fractal.

FIGS. 52C and 52D are plots of information units and capacity,respectively, against magnification for the Vicsek fractal.

FIGS. 52E and 52F are plots of information units and capacity,respectively, against magnification for a dendritic structure withfractal dimension 1.7.

FIGS. 53A and 53B are plots showing capacity against magnification for afractal pattern of fractal dimension 1.7.

FIGS. 54A-54D are schematic diagrams of a dendritic pattern.

FIG. 55 is a schematic diagram of a dendritic pattern analyzed using abox counting technique.

FIGS. 56A and 56B are plots of capacity against magnification for afractal pattern analyzed according to a quaternary coding scheme.

FIG. 57A is a schematic diagram of a dendritic structure.

FIG. 57B is a schematic diagram of a portion of the dendritic structureof FIG. 57A shown in a magnified view.

FIG. 58 is a plot of information capacity against number of parametersfor a dendritic structure

FIG. 59 is a schematic diagram of a dendritic structure analyzed using aCartesian coding technique.

FIG. 60 is a plot of a ratio of pattern to grid locations against thenumber of grid locations for a grid coding technique.

FIG. 61 is a schematic diagram showing a branching structure.

FIG. 62 is a schematic diagram showing a decision tree.

FIG. 63 is a schematic diagram showing a dendritic structure analyzedusing a polar coding technique.

FIG. 64 is a schematic diagram showing a dendritic structure analyzedusing a different polar coding technique.

FIGS. 65A-65C are schematic diagrams showing dendritic structures withvarying levels of damage.

FIGS. 66A-66D are schematic diagrams showing dendritic structures withfiducial markings.

FIG. 67 is an image showing a copper dendritic structure grownunderneath the surface of a material.

Like reference symbols in the various drawings indicate like elements.

DETAILED DESCRIPTION

Dendritic structures appear in a wide variety of natural forms,including, for example, lightning, dielectric breakdown, the flow ofrivers, mechanical fractures, and blood vessels. Typically, theparticular forms of these dendritic structures are a product of thephysical processes that give rise to them and a component of randomnessinherent to flow processes. This disclosure introduces dendriticstructures by describing certain features thereof and methods for makingsuch structures, including methods for fabricating dendritic structuresthat are suitable for large-scale manufacturing. Subsequent sections ofthis disclosure discuss a variety of applications for dendriticstructures, including the use of dendritic structures in commercialtransactions.

Fabrication of Dendritic Structures

One example of a dendritic structure is shown in schematic top view inFIG. 1.

Dendritic structure 134 is disposed on a substrate 170. Althoughdendritic structures in nature form by a wide range of physical andchemical processes, metallic dendritic structures have a number ofproperties that are advantageous for various applications. For example,metallic dendritic structures can be simply formed and “read”electrically and/or optically and/or using other non-destructivemeasurement methods (for example, using X-ray fluorescence (XRF)methods). Accordingly, dendritic metal structures are useful in many ofthe applications disclosed herein.

Due to their multi-branched, stochastically grown structure (as will bedescribed further herein), dendritic metal structures can provide aneffectively unique, randomly generated identifier. Moreover, dendriticmetal structures can also be made to have “nanoscale” features in theirindividual conducting elements, which allows them to contain orrepresent a great deal of information in a relatively small area.Moreover, as will be described in more detail below, because dendriticmetal structures can be formed using deposition from a solidelectrolyte, the fabrication of such devices can be relatively simpleand therefore of low cost. Dendritic metal structures suitable for usein the methods described herein are described generally in U.S. Pat. No.8,345,910, U.S. Patent Application Publication No. US 2011/0254117, andInternational Patent Application Publications Nos. WO 2012/065076 and WO2012/065083, the entire contents of each of which are incorporated byreference herein.

A photomicrograph of an example of a dendritic metal structure is shownin FIG. 2, in which dendritic silver structures are grown from a nickelcathode. FIG. 3 is a profilometry measurement of another example of adendritic metal structure. In general, a dendritic metal structure has amulti-branched structure formed of segments of reduced metallicmaterial. In certain embodiments, dendritic metal structures have anaverage individual segment width (i.e., in the plane of the dendriticmetal structure) of no more than about 300 μm (e.g., no more than about100 μm, no more than about 10 μm, no more than about 1 μm, or even nomore than about 200 nm). In certain embodiments, dendritic metalstructures have an average individual segment width of at least about 20nm.

In some embodiments, dendritic metal structures have an averagethickness (i.e., normal to the plane of the dendritic metal structures)of no more than about 100 μm (e.g., no more than about 10 μm, no morethan about 5 μm, no more than about 500 nm, no more than about 200 nm,or even no more than about 50 nm). In certain such embodiments,dendritic metal structures have an average thickness of at least about10 nm.

The areas of dendritic metal structures can range from several mm² tomicro- or even nano-scale dimensions, depending on the method offabrication and the application for which the structures are used.Dendritic metal structures can include one or a plurality ofseparately-nucleated branched structures, as described in more detailbelow.

Dendritic metal structures can be formed from a variety of metallicmaterials. Metals such as silver and copper can be particularly usefulas they are highly mobile in a variety of materials and are readilyreduced and oxidized so the electrochemical aspects of the fabricationprocess are relatively straightforward. Silver is especially appropriatefor dendritic structure growth applications due to its nobility and easeof both reduction and oxidation. Accordingly, in certain embodiments,dendritic metal structures are formed from silver. Dendritic metalstructures can also be formed, for example, from copper, from zinc,and/or from iron. Dendritic metal structures can also be formed frommultiple metals to make duplication of such structures more difficult.

Dendritic metal structures can be formed by electrodeposition in an ionconductor (i.e., an electrolyte) by generating an ion current in the ionconductor and using the flow of ions to build up the dendritic structurein or on the ion conductor via electrochemical processes. The ionconductor can be liquid, gel, or solid, or a combination thereof.

A sustained ion current will only flow through the ion conductor ifthere is a source of ions at one point and a sink of ions at another.The process of electrodeposition, in which metal cations in theelectrolyte are reduced by electrons from a negative electrode (e.g., acathode), is essentially an ion sink as ions are removed from theelectrolyte to become atoms. However, in the absence of an ion source,the reduction of the ions at the cathode occurs at the expense of theelectrolyte. The concentration of ions in the solid electrolytetherefore decreases during electrodeposition until the electrodepotential equals the applied potential and reduction will cease.

It is therefore desirable in certain embodiments to have an oxidizablepositive electrode (e.g., anode)—one which can supply ions into theelectrolyte to maintain ion concentration and overall charge neutrality.In the case of a silver (or copper) ion-containing electrolyte, theoxidizable anode can be implemented merely as a solid silver (or copper)member, or a member formed from a compound or alloy containing freemetal.

The anode will oxidize when a bias is applied if the oxidation potentialof the metal is greater than that of the solid solution. Under steadystate conditions, as current flows in the solution, the metal ions willbe reduced at the cathode. For the case of silver, the electrodereactions are:

Ag→Ag⁺ +e ⁻  Anode:

Ag⁺ +e ⁻→Ag  Cathode:

with the bias being supplied by an external power source.

The deposition of Ag metal at the cathode and partial dissolution of theAg at the anode indicates that fabrication of the dendritic structure isanalogous to the reduction-oxidation electrolysis of metal from anaqueous solution, except that when a solid electrolyte is used infabrication (e.g., rather than a solution of ions), the anions are fixedin position. Accordingly, when a bias is applied across the electrodes,silver ions migrate toward the cathode under the driving force of theapplied field and the concentration gradient. At the boundary layerbetween the electrolyte and the electrodes, a potential differenceexists due to the transfer of charge and change of state associated withthe electrode reactions. This potential difference, typically in theorder of a few hundred millivolts, leads to polarization in the regionclose to the phase boundary, known as the double layer. Even though thevoltage associated with the polarization is small, structures with along, thin region of solid electrolyte between the electrodes typicallyrequire higher voltages to initiate electrodeposition as most of theapplied voltage will be dropped across the high resistance electrolyte.For example, the polarization-resistance of a 10 μm² electrode will bearound 10⁹Ω, but if a 50 nm thick 100 Ω·cm Ag—Ge—Se electrolyte betweenanode and cathode is 10 μm wide and 100 μm long, the series resistancewill be twice this value and so at least 0.75 V is typically used togenerate a 0.25 V drop at the cathode to cause electrodeposition.

As in any plating operation, the ions nearest the electron-supplyingcathode will theoretically be reduced first. However, in real-worldfabrication processes in which the nanoscale roughness of the electrodesis significant and the fields are relatively high, statisticalnon-uniformities in the ion concentration and in the electrodetopography can promote localized deposition or nucleation rather thanblanket plating. Even if multiple nuclei are formed, the nuclei with thehighest field and best ion supply will be favored for subsequent growth,extending out from the cathode as individual elongated metallicfeatures. The deposition interface continually moves toward the anode,increasing the field and thereby speeding the overall growth rate of theelectrodeposit. Without wishing to be bound by theory, it is believedthat the addition of new atoms to the growing electrodeposit occursthrough a diffusion-limited aggregation mechanism.

The electrodeposition of metal on the cathode does not mean that ionsentering from the oxidizable anode have to travel the entire length ofthe structure to replace those that are reduced. For example, in solids,the ions move through the electrolyte by a coordinated motion in whichthe ion closest to the reduced ion will move to the vacated negativesite on the hosting material and those upstream will do likewise, eachfilling the vacated site of the one downstream, until the last vacatedspace closest to the anode is filled by the incoming ion. So, in theinitial stages of deposition, the electrodeposit is actually made up ofreduced ions from the electrolyte itself but since each ion deposited onthe growing electrodeposit corresponds to one that has been removed fromthe metal source, the net effect is a shift of mass from the anodetoward the cathode. In general, the growth process in these structuresis more complex than a simple plating operation as the depositioninterface is moving toward the source of the ions. Since theelectrodeposit is physically connected to the cathode, it can supplyelectrons for subsequent ion reduction, so the growing electrodepositwill harvest ions from the electrolyte, plating them onto its surface toextend itself outwards from the cathode. This has two consequences: thegrowth interface continually moves out to meet the ions, and the growthcloses the gap between the electrodes thereby increasing the field. Bothof these help to speed the overall growth rate of the deposit.

Without wishing to be bound by theory, in the most general case, it isbelieved that the process of deposit formation starts with thenucleation of the new metal atom phase on the cathode and the depositsdevelop with a structure that generally follows a Volmer-Weber 3-Disland growth mechanism. The addition of new atoms to the growingdeposit occurs due to a diffusion-limited aggregation (DLA) mechanism,as described for example in T. A. Witten and L. M. Sander, Phys. Rev.Leu. 47: 1400 (1981). In this growth process, an immobile “seed” isfixed on a plane in which particles are randomly moving. Particles thatmove close enough to the seed in order to be attracted to it attach andform the aggregate. When the aggregate consists of multiple particles,growth proceeds outwards and with greater speed as the new depositsextend to capture more moving particles. Thus, the branches of the coreclusters grow faster than the interior regions. The precise morphologydepends on parameter such as the potential difference and theconcentration of ions in the electrolyte, as described for example in Y.Sawada, A. Dougherty, and J. P. Gollub, Phys. Rev. Lett. 56: 1260(1986).

At low ion concentrations and low fields, the deposition process isdetermined by the (non-directional) diffusion of metal ions in theelectrolyte and the resulting pattern is fractal in nature. For high ionconcentrations and high fields as are common in the methods describedherein, the moving ions have a strong directional component, anddendritic structure formation occurs. The dendritic structures have abranched morphology, but grow along a preferred axis largely defined bythe applied electric field. As an example, FIG. 7 shows dendritic metalstructures grown between parallel electrodes (i.e., an anode at the topof the figure and a cathode at the bottom of the figure).

The complexity of the dendritic form in two dimensions is evident fromimages such as shown in FIG. 7. The stochastic growth process ensuresthat the shape of every newly-grown dendritic structure is truly unique.It should be noted, however, that the growth process is generally threedimensional. When a dendritic structure forms inside a solidelectrolyte, there are no restrictions on growth direction and thestructure will typically branch out like a tree to fill a volume, buteven when electrodeposition occurs on the surface of a solid ionconductor, there is still an “upward” component of growth, i.e., in adirection normal to the surface. This occurs because, in addition to thelateral growth across the surface, there is electrodeposition at theinterface between the ion conductor and the metal dendrite. This basaldeposition pushes the earlier-deposited material upwards, resulting in ananoscale “mountainous” three-dimensional form. This form is shown inFIG. 4, which is a scanning electron micrograph of the edge of a silverdendritic structure on a silver-doped chalcogenide glass. The micro- andnano-scale facets of such 3-D features are once again formed viastochastic processes and introduce yet another layer of complexity (andrandomness) to the overall structure.

In some embodiments, dendritic metal structures are formed by methodsthat include providing an ion conductor and two or more electrodes incontact with the ion conductor, and applying a bias voltage across theelectrodes sufficient to grow the dendritic metal structure in or on theion conductor. Methods for growing dendritic metal structures aredescribed generally in U.S. Pat. No. 8,345,910, U.S. Patent ApplicationPublication No. US 2011/0254117, and International Patent ApplicationPublications Nos. WO 2012/065076 and WO 2012/065083.

The stochastic nature of the electrodeposition process leads torandomly-branched and randomly-faceted patterns each time a dendriticstructure is grown on a new region of an ion conducting medium. As willbe discussed subsequently, as a result of their random and uniquenature, these dendritic structures can be used to generate uniqueidentifiers that are useful in a variety of applications, includingobject identification and tracking, and data encryption. The methods andapparatus used to create these patterns is straightforward and thematerials involved can be placed on a variety of substrates, includingpliable and/or flexible materials. Examples of device formats andmethods for generating dendritic structures are described subsequentlyin greater detail.

A wide variety of ion conductors can be used, for example, includingsolid films (e.g., oxides/chalcogenides), gels, and liquids. For certainapplications, it can be desirable to use a solid ion conductor. Solidion conductors are useful due to their mechanical and chemical stabilitywhich allows them to be used in the field with minimal encapsulation.Examples of solid ion conductors suitable for use in certain embodimentsinclude “superionic” solid electrolytes (fast ion conductors) and/orother materials such as oxides which have suitable ion mobility.

Dendritic metal structures can be formed by deposition from a solidelectrolyte. In certain embodiments, the solid electrolyte includessilver or copper ions, as such materials tend to have high ion mobilityand can be less difficult to make than alkali metal solid electrolytes.Silver is also well-suited for electrode growth applications due to itsmobility and ease of both reduction and oxidation. In some embodiments,copper-containing solid electrolytes can be used to form dendriticcopper structures. For example, crystalline Ag halides, principally AgI,and silver chalcogenides, e.g., Ag₂S, Ag₂Se, and Ag₂Te, and their coppercounterparts, can be used as solid electrolytes.

The layer of solid electrolyte can be, for example, a metal-containingchalcogenide glass (i.e., containing oxygen, sulfur, selenium and/ortellurium, although oxide glasses are often treated separately from theothers in the literature). Chalcogenide glasses can be formed with awide range of physical characteristics and can be made using a varietyof techniques, such as physical vapor deposition, chemical vapordeposition, spin casting and melt quenching. The tellurides exhibit themost metallic character in their bonding and are the “weakest” glassesas they can crystallize very readily (hence their use in so-called phasechange technologies such as re-writable CDs and DVDs) and the othersexhibit an increasing glass transition temperature going further upGroup VI of the periodic table, with oxides having the highest thermalstability. Stable binary glasses can, for example, include a Group IV orGroup V element, such as germanium or arsenic, with a wide range ofatomic ratios possible. The bandgaps of the chalcogenide glasses rangefrom about 1-3 eV for telluride, selenide and sulfide glasses, to 5-10eV for the oxide glasses. The non-oxide glasses are typically moreflexible than oxide glasses, but more rigid than organic polymers; otherphysical properties follow the same trend. Such structural flexibilitycan result in the formation of voids through which ions can readily movefrom one equilibrium position to another. It can also allowchalcogenides glasses to be used with flexible substrates.

In some embodiments, a solid electrolyte formed of Ag-doped Ge₃₀S₇₀ isused for dendritic structure fabrication. In other embodiments,different materials can be used as the solid electrolyte. For example,silver- or copper-doped oxide glasses such as SiO₂ or transition metaloxides can be used in harsher operating environments. Such glasses canwithstand higher processing temperatures, are more resistant tomechanical abrasion and chemical damage, and can provide highertransmission over the visible wavelength range than the higherchalcogenide glasses, but may provide slower dendritic structure growthdue to lower ion mobility.

In certain embodiments, the chalcogenide glass is a germaniumchalcogenide glass. Germanium chalcogenides have relatively lowcoulombic energies and relatively low activation energies for iontransport. Germanium chalcogenides are desirably glassy in nature; ionconductivity can often be greater in glassy materials than in thecorresponding crystalline materials. Of course, crystalline orsemi-crystalline materials can also be used. Germanium chalcogenidesalso tend to be relatively soft materials, making them suitable for usein certain methods in which the dendritic metal structure is formed,annealed or otherwise moved to the interface between the solidelectrolyte and the electrically active structure, as described in moredetail below. Germanium chalcogenides are also relatively flexible, andcan be used on flexible devices. Accordingly, in some embodiments,devices that include the fabricated dendritic structure(s) are flexible.These mechanical properties of the germanium chalcogenides also helpavoid cracking during thermal expansion and mechanical stress duringuse.

In certain embodiments, the solid electrolyte includes a solid solutionof As_(x)S_(1-x)—Ag, Ge_(x)Se_(1-x)—Ag, Ge_(x)S_(1-x—)—Ag,As_(x)S_(1-x)—Cu, Ge_(x)Se_(1-x)—Cu, Ge_(x)S_(1-x)—Cu, where x rangesfrom about 0.1 to about 0.5, other chalcogenide materials incorporatingsilver, copper, zinc, iron, combinations of these materials, Ag- andCu-doped transition metal oxides, Ag- and Cu-doped silicon or germaniumoxides, and the like. Photodissolution techniques can be used to loadmetal and/or metal ions into the solid electrolyte.

In some embodiments, the solid electrolyte includes a germanium-selenideglass with about 10 to about 50 atomic percent silver diffused in theglass (e.g., Ag₃₃Ge₂₀Se₄₇). Such materials can be formed usingevaporation. Additional solid electrolyte materials and methods offorming them are discussed in U.S. Pat. No. 6,635,914, the entirecontents of which are incorporated herein by reference.

As one example of the fabrication of the solid electrolyte, a 50 nmlayer of Ge_(0.20-0.04)Se_(0.80-0.60) is first deposited onto thesurface of an electrically active structure, and the Ge—Se layer iscovered with about 20 nm of silver. The silver is dissolved into theGe—Se glass by exposing the silver to a light source having a wavelengthof about 405 nm and a power density of about 5 mW/cm² for about tenminutes. Any excess silver is then removed using a Fe(NO₃)₃ solution.The solid electrolyte material is then patterned and etched usingreactive ion etching (RIE) (e.g., CF₄+O₂) or wet etching (e.g., usingNaOH:IPA:DI).

The addition of metallic elements such as silver or copper to achalcogenide glass transforms it into an electrolyte, as silver andcopper atoms can form mobile cations within the chalcogenide glassmaterial. The ions are associated with the non-bridging chalcogen atomsbut the bonds formed are relatively long. As with any coulombicattraction, the coulombic energy is proportional to the inverse of thecation-anion distance, so long bonds lead to reduced attractive forcesbetween the charged species. The Ge-chalcogenide glasses are thereforeamong the electrolytes with the lowest coulombic energies. Thermalvibrations will allow partial dissociation, which results in a two-stepprocess of defect formation followed by ion migration. The activationenergy for this process strongly depends on the distance between thehopping cation and the anion located at the next nearest neighbor aswell as the height of the intervening barrier. In addition to having lowcoulombic energies, the Ge-chalcogenides also have relatively lowactivation energies for ion transport. In this respect, the existence ofchannels due to the structure of the electrolyte is critical in the iontransport process. As an example of this effect, the Ag⁺, conductivityin glassy AgAsS₂ is a factor of 100 larger than that in the crystallinecounterpart due to the more “open” structure of the non-crystallinematerial.

The rigidity and bonding character of the oxide electrolytes means thattheir ion mobility is typically orders of magnitude lower than that ofthe Ge-chalcogenides but this also results in higher thermal, chemical,and mechanical stability. Increased stability suggests that Ag- orCu-doped oxide glasses, such as SiO₂ or many of the transition metaloxides (e.g., WO₃), may be more suitable for harsher operatingenvironments.

Other electrolyte materials can also be used in the fabrication methodsdisclosed herein. As suggested above, tellurides (e.g., doped germaniumtellurides) can also be used in certain embodiments. In someembodiments, the solid electrolyte is a metal (e.g., copper) dopedtransition metal oxide.

The solid electrolyte material can have a thickness, for example, in arange of about 1 nm to about 1 μm. In certain embodiments, the layer ofsolid electrolyte has a thickness in the range of about 5 nm to about100 nm. In some embodiments, the solid electrolyte has a thickness lessthan about 10 nm. For example, the solid electrolyte can have athickness in the range of about 1 nm to about 10 nm. Where the solidelectrolyte has low transmissivity at desired wavelengths, use ofthinner solid electrolyte layers can improve overall transmission to theelectrically-active layer. Such solid electrolyte layers need not becompletely continuous on the micro- or nano-scale, as reduced sheetresistance can be achieved even with discontinuous dendritic structures.Moreover, thinner solid electrolyte layers can be more flexible,allowing for increased process and device flexibility. The sold ionconductor may be deposited on the substrate and retained after growthbut may also be removed (i.e., before use) to ensure that the dendriticpattern cannot be altered unintentionally after fabrication.

In certain embodiments, the dendritic metal structure is disposed at theinterface between a substrate and the electrolyte. For example, in theembodiment shown in the schematic side cross-sectional view of FIG. 9,electrical device 700 includes a cathode 732 disposed at the interfacebetween the substrate 710 (on second substrate 720) and a solidelectrolyte 740. A sacrificial anode 746 is positioned, for example, ontop of the solid electrolyte. To prevent deposition on top of the solidelectrolyte, a growth retarding layer 750 (e.g., a hard oxide layerchemically bound to or oxidatively grown from the top of the electrolytelayer) can be formed thereon. A dendritic metal structure 734 can beformed at the interface between the solid electrolyte and theelectrically active structure by the application of a bias. In certainembodiments, the solid electrolyte is a relatively soft glass (e.g., agermanium chalcogenide glass such as silver-doped germanium arsenide orselenide), which can deform slightly to allow the dendritic metalstructure to grow at the interface. In such embodiments, the dendriticmetal structure can have good electrical contact with the electricallyactive structure, as there is substantially no solid electrolytedisposed therebetween.

In some embodiments, a liquid or gel electrolyte is used for dendriticstructure fabrication. Liquid or gel electrolytes are easier to removeafter growth and so may be more suitable for tags which only contain thedendritic structure but not the ion conductor in the field. If a liquidsor gel electrolyte is to be a permanent (or semi-permanent) part of afabricated device, the device may include additional layers to containand protect the electrolyte, as will be discussed in greater detailsubsequently.

FIG. 5 is a schematic diagram showing one embodiment of a method forfabricating dendritic structures using a liquid or gel electrolyte. Themethod is described herein with respect to a liquid electrolyte, but itshould be appreciated that similar steps can be performed in conjunctionwith the use of a gel electrolyte. A substrate 410 having a surface 412and a cathode 422 disposed thereon is provided. Also provided is ananode 424 formed from a metal; in this embodiment, the anode is alsodisposed on surface 412 of the substrate 410. A liquid 430 in which themetal of the anode is at least partially soluble (i.e., in some cationicform) is then disposed on the surface of the substrate. As shown in FIG.5, in this embodiment, the liquid is simply disposed as a relativelythin film on the surface of the substrate, held in place by surfacetension. The liquid is in electrical contact with both the anode 424 andthe cathode 422. A bias voltage is applied across the cathode and theanode sufficient to grow the dendritic metal structure 440 extendingfrom the cathode.

Anode 424 and cathode 422 are positioned relative to substrate 410 sothat the dendritic metal structure can be electrodeposited. As thedendritic metal structure grows from the cathode, it is disposed on theon the surface of the substrate. The anode can be, for example, alsodisposed on the surface of the substrate. In such embodiments, the anodecan help to direct the growth of the dendrite.

In other embodiments, the anode is not disposed on the substrate, butrather is in contact with the liquid. In such embodiments, the anodecan, for example, be positioned within 1 cm, or even 5 mm of thesurface. For example, FIG. 6 shows an embodiment in which the anode 524is not disposed on the surface 512 of the substrate 510, but rather issuspended slightly above it. In this example, the liquid 530 is providedin a relatively large volume (i.e., in tank 550, in which the substratebearing the cathode 522 and the anode are also disposed).

In certain embodiments, the anode can be placed (i.e., not deposited,such as in the form of a separate piece of metal) on the surface, thenremoved from the surface after deposition. In such embodiments, theanode can help to direct the directionality of growth, as describedabove, but can easily be removed.

In some embodiments, the anode and/or the cathode are placed on thesurface of the substrate, but are not deposited thereon. For example,either the anode or the cathode or both can be placed or held in contactwith the surface, so as to provide directionality to the growth of thedendritic metal structure, but can be easily removed once growth iscomplete.

In the process of electrodeposition, metal cations in the liquid arereduced at the cathode. To replace the metal cations in the liquid andallow for continued growth of the dendritic metal structure, the anodecan include the same metal as the metal of the dendritic metalstructure. As the dendritic metal structure grows by reduction at thecathode, the anode is concomitantly oxidized and dissolved into theliquid, resulting in a net mass transfer from the anode to the growingdendritic metal structure. For example, the anode can be formed ofsilver, a silver alloy, copper or a copper alloy. When the metal isprovided by the anode, the liquid need not have any metal ions dissolvedin it when it is disposed on the surface of the substrate. By physicallychanging the anode material during growth, or by providing an electricalbias in sequence to anodes of differing composition, it is possible togrow a dendritic structure that includes multiple metals either as amixture or as segments in the structure. Fabricating dendriticstructures in this manner makes subsequent replication of the structures(i.e., in a separate growth process) very difficult.

In some embodiments, the anode need not dissolve into the liquid, andthe dendritic metal structures can be grown only from the metalinitially dissolved into the liquid. For example, the anode can berelatively inert, as described below with respect to the cathode. Insuch embodiments, a relatively large volume of liquid can be provided inorder to supply the desired amount of metal cations.

In certain embodiments, it is possible that the ion conductor is notactually a part of the device structure but is instead incorporated in a“writing” apparatus. In such embodiments, the dendritic structure can bephysically transferred to the substrate or otherwise retained on thesubstrate after growth at the electrolyte-substrate interface.Similarly, in some embodiments, the electrodes are not part of thedevice and are instead mounted on the apparatus that applies the voltageto the ion conductor, thereby simplifying the device structure.

A transparent layer can be disposed over the dendritic metal structureto protect the electrodeposit from damage and help to preventduplication of the structure by the use of impression/moldingtechniques. This layer can be engineered to allow the growth of thedendritic metal structure at the interface between the ion conductor andthe protective film or it may be applied after growth. The transparentlayer can be, for example, a layer of transparent polymer, or a layer ofdeposited material such as an oxide or nitride of silicon, titanium orgermanium.

In general, substrates used to support the dendritic structure can berigid or flexible, and a wide range of different materials havingdifferent mechanical properties can be used as substrates. Typically,appropriate ion conductors and electrode materials are selected based onthe type of substrate that is used.

While a wide range of substrate materials, from insulators toconductors, may be used, in some embodiments an additional barrier layermay be used to prevent interaction between certain substrates and theion conductor. Thus, the barrier layer is disposed between the substrateand the dendritic metal structure. Accordingly, the barrier layer can bebetween the ion conductor and the substrate during the electrodepositionoperation.

Examples of suitable rigid (or semi-rigid) substrates include glass,hard plastic, metals, and semiconductors. Dendritic structures anddevices that include such structures can be formed on integratedcircuits (either on the chip itself or outside the package). Examples offlexible substrates include plastic sheets, metal foils, smooth paper,and coated close-weave fabrics.

Electrodes allow the voltage to be applied to the ion conductor toinduce the flow of ions and activate the redox processes necessary forelectrodeposition. The electrode materials may be deposited andpatterned using a variety of methods including sputtering/etching,lift-off, shadow masking, screen printing, and standard (roll-to-roll)printing using conductive inks. A wide range of viable electrodepatterns is possible, including parallel, concentric, and multi-contactconfigurations.

In some embodiments, an anode and a cathode can be formed in contactwith a solid electrolyte so that the dendritic metal structure can beelectrodeposited. In the process of electrodeposition, metal cations inthe electrolyte are reduced at the cathode. To replace the metal cationsin the electrolyte and allow for continued growth of the dendritic metalstructure, the anode can include the same metal as the metal of thedendritic metal structure and the solid electrolyte. As the dendriticmetal structure grows by reduction at the cathode, the anode isconcomitantly oxidized and dissolved into the solid electrolyte,resulting in a net mass transfer from the anode to the growing dendriticmetal structure. For example, the anode can be formed of silver, asilver alloy, copper or a copper alloy. In other embodiments, the anodeneed not dissolve into the solid electrolyte, and the dendritic metalstructures can be grown only from the metal initially dissolved into thesolid electrolyte. For example, the anode can be relatively inert, asdescribed below with respect to the cathode.

In certain embodiments, the cathode can be relatively inert andgenerally does not dissolve during the electrodeposition operation. Forexample, the cathode can be formed from an inert material such asaluminum, tungsten, nickel, molybdenum, platinum, gold, chromium,palladium, metal silicides, metal nitrides, and doped silicon. Ofcourse, in other embodiments, the cathode need not be formed from aninert material. Indeed, when both electrodes are formed from the metalof the dendritic metal structures, either electrode can act as the anodefrom which the dendritic metal structures grow, providing additionalprocess flexibility. Appropriate cathode materials can be selected basedon the desired electrodeposition conditions. Various configurations ofsolid electrolyte and electrodes suitable for use in the methodsdisclosed herein are discussed, for example, in U.S. Pat. No. 6,635,914.

Contacts may be electrically coupled to the anode and/or cathode tofacilitate forming electrical contact to the respective electrodes.Contacts can be formed of any conductive material and are preferablyformed of a metal such as aluminum, aluminum alloys, tungsten, orcopper. Generating the dendritic pattern typically involves theapplication of a small voltage (e.g., 0.1 to 10 V) to the electrodes incontact with the ion conducting film.

In some embodiments, the fractal dimension of the dendritic structure(i.e., its effective density) can be controlled via the magnitude of theapplied voltage; however, the specific shape of the structure istypically random. In certain embodiments, multiple electrodes can beused to generate multiple dendritic forms to fabricate more complexshapes and produce large area dendritic structures. Use of a pluralityof dendritic structures in various applications can provide can providefor information redundancy, e.g., in the event that one of the dendriticstructures is damaged.

Fabrication of dendritic structures can occur in a variety of contextsand applications. In some embodiments, dendritic structure growth can beperformed during manufacture of a tag or device that uses or includesthe dendritic structure. In certain embodiments, dendritic structuregrowth can be performed by user, e.g., during implementation of anapplication of dendritic structure. In this scenario, the ion conductorcan be retained within the device. Conversely, when the dendriticstructure is grown during device manufacturing, the fabrication processcan be performed with a removable ion conductor. Moreover, provided theelectrodes and the ion remain in place, additional growth of thedendritic structure can be performed following manufacture (e.g., duringimplementation of an application) to deliberately alter an existingdendritic structure.

In some embodiments, when a sufficient bias (e.g., a hundred mV or more)is applied across the anode and the cathode, metallic ions (e.g., Ag⁺)to move from the anode (in this example, made of silver) and/or frommetal dissolved in the solid electrolyte toward the cathode. Metallicions at the cathode are reduced to form the dendritic metal structure,which grows and extends from the cathode out onto the solid electrolyte.The amount of electrodeposited material is determined by factors such asthe applied voltage, the nature of the metal, the ion current magnitudeand the time during which the current is allowed to flow. The dendriticmetal structure can be deposited within or on the layer of solidelectrolyte as an increased concentration of reduced metal compared tothe concentration of such material in the bulk solid electrolytematerial. Electrodeposits can have significant growth parallel to aswell as normal to the solid electrolyte surface. The applied biasvoltage can typically be, for example, in the range of 200 mV to 20 V,but other bias voltages can also be used.

Dendritic structure growth causes a mass transfer of metal from thesolid electrolyte to the growing dendritic structure. For example, whenthe solid electrolyte has a metallic sheen due to excess metal, thegrowth process can transfer that metal to the dendritic structure,thereby increasing the apparent transmission of the solid electrolyte.When the solid electrolyte is not replenished with metal (e.g., by asacrificial electrode), dendritic structure growth can significantlydeplete the solid electrolyte of metal. Depletion of metal in the solidelectrolyte can also occur when metal dissolves into the solidelectrolyte from the anode much more slowly than it is plated onto thedendritic metal structures. In general, the bias voltage applied betweenthe anode and cathode can be reversed to redissolve metal from thedendritic structures, thereby providing a method to more precisely tunethe extent of dendritic structure growth.

In certain embodiments, the metal ions can, for example, be provided bythe anode. For example, the anode can be formed from the metal dissolvedin the solid electrolyte, and the metal of the anode dissolves into thesolid electrolyte as the dendritic metal structure is grown.

Reading Dendritic Structures

Dendritic structures fabricated according to the methods disclosedherein can be used for a variety of applications. Many such applicationsinvolve “reading” the structures, which refers to a process ofidentifying features of the structures which uniquely identify thestructures. In this manner, particular dendritic structures can bedistinguished from other dendritic structures, allowing dendriticstructures to be used in a variety of identification, tagging, tracking,and encoding applications. Because electrodeposited dendritic structuresare fractal in nature and possess increasing complexity as the scale isdecreased, the complexity of specific identifiers (e.g., numbers orcodes) generated from dendritic structures depends on the resolution ofthe reading techniques.

This section of the disclosure will describe a variety of methods forreading dendritic structures. Certain methods will also be described inmore detail later in the disclosure, in some cases in the context ofspecific applications.

In some embodiments, dendritic structures can be read optically. Toimplement optical reading, the pattern of the dendritic structure isinterrogated using light, which can include wavelengths within and/oroutside the visible spectrum, to produce a unique signal. For example,camera imaging may be used to obtain a detailed picture of the dendriticpattern. The acquired pattern can then be algorithmically analyzed toproduce a unique code or identifier associated with the dendriticstructure that acts as a type of “fingerprint”. CCD (charge-coupleddevice) or CMOS (complementary metal-oxide semiconductor) cameras can beused to capture images that are analyzed to identify the dendriticstructure.

Various levels of detail may result from optical imaging, depending onthe magnification and numerical aperture of the lenses used. Forexample, using a lens with a high numerical aperture, the focal planemay be swept along the z-axis (i.e., the axis normal to the main surfaceover which the dendritic structure extends) to reveal fine topographicaldetails of the dendritic pattern.

The nature of the light used also affects the type of information thatis obtained from the reading process. Laser or bright incoherentillumination light typically produces a particular light scattering(diffuse) pattern via reflections from the various facets of theelectrodeposit that can be analyzed either by a camera or an array ofphotodetectors. Infrared and ultraviolet illumination (down to the x-rayregime) can also be employed along with detector arrays that aresensitive to these wavelengths.

In certain embodiments, reading the dendritic structure is performedusing X-ray fluorescence spectroscopy. X-ray fluorescence (XRF) is anon-destructive measurement method that can be used to characterize thecomposition of materials, based on the emission of characteristic“secondary” (or fluorescent) x-rays from a material that has beenexcited by bombardment with high-energy x-rays or gamma rays.

In some embodiments, dendritic structures can be read electrically. Forexample, electrical reading can be used when optical reading isimpractical due to the structure being embedded within an object, orwhen a direct electrical readout is desirable (e.g., when the dendriticstructure is used with an integrated circuit).

Capacitance reading can be performed using an two dimensional array ofsensors which measure the local changes in electrical capacitance causedby the presence of the branches of the dendritic pattern and convertthis to an electrical output (similar technology is also used forfingerprint recognition, using a capacitive “touch” sensor). The sensorarray can, for example, be part of a reading device and/or can bepermanently incorporated in the pattern generating device, the latterbeing particularly appropriate if the pattern generator is embedded in aproduct such as an integrated circuit. A schematic view of oneembodiment of a general electrical reading apparatus is shown FIG. 8.

Resistance or impedance can also be detected at points across a surfaceusing the sensor array apparatus shown in FIG. 8. To measure resistanceor impedance, an electrical contact is typically formed between the(conducting) dendritic structure and the sensor array to allow a smallcurrent to flow and thereby be detected by suitable sense amplifiers.

In some embodiments, frequency modulated radio frequency waves can alsobe used to read a conductive dendritic pattern. Different branch shapeswill respond to different frequencies, producing distinctive peaks andtroughs in the transmitted and reflected frequency spectra. Accordingly,the dendritic structure can be used in a radio frequency identification(RFID) scheme, for example, by being coupled to (e.g., directly orindirectly connected to) a suitable radio frequency antennae or othersource of radio-frequency waves. Different dendritic structures willprovide different resonant frequencies, and thus different reflectedfrequencies or electromagnetic signals. For example, methods for readingdendritic structures can include illuminating the dendritic structurewith radio waves of different frequencies, and detecting one or morefrequencies of the reflected radio waves. Methods for reading dendriticstructures can also include, for example, direct coupling of anelectromagnetic signal (e.g., at radio frequencies) into the dendriticstructure, and measuring an electromagnetic signal from the dendriticstructure at one or more radio frequencies to read the dendriticstructure.

Other methods for reading dendritic structures can also be used. Forexample, ultrasonic techniques can be used to read the basic form of thedendritic structure, which may be sufficient for some applications.Moreover, a combination of multiple reading techniques (e.g., orthogonalmulti-readout detection and identification) provides enhanced accuracyand additional security against the forgery of the dendritic structure.

The reading methods disclosed herein can be used in the identificationand authentication of objects, the encryption of data, and to accessencrypted data. For example, in some embodiments, methods foridentifying an object that feature a dendritic structure include readingthe dendritic structure to provide a signal, generating a uniqueidentifier from the signal, and identifying the object using the uniqueidentifier. The unique identifier can be, for example, a binary number,a text string, a set of analog values, or an image of the dendriticstructure. In certain embodiments, the unique identifier can begenerated by applying a numerical method (e.g., a mathematicalalgorithm) to the signal provided by the reading of the dendriticstructure, and generating the unique identifier using the numericalmethod. The numerical method can be any suitable method that convertsdata from the reading process into a suitable unique identifier. Incertain embodiments, the numerical method uses data from two independentreading techniques as described above. The numerical method can beperformed by a computer (i.e., it can be a computer-implementednumerical method). Computer-implemented numerical methods can beperformed by a suitably-programmed general purpose computer, forexample, or by a microprocessor or other circuit specifically adapted toperform the method.

Currently, many objects are marked with an identifier such as a barcode, but these codes are the same for every copy of the object and sothere is no way to track individual objects, unless a unique serialnumber is included on the object and also read. The unique dendriticstructures disclosed herein can be fabricated and read using thetechniques described herein, allowing the tracking of individualobjects. Since there are a vast number of dendritic structures that canbe produced using a few square millimeters of surface, it is feasible toinconspicuously tag every object to be tracked with its own dendriticstructure-based identifier. The unique identifier generated from thedendritic structure can be stored in a database that links theinformation to details of the object's manufacture, specificcharacteristics, last known location, etc. Tracking objects in thismanner is particularly important for high value/high demand items, andtracking also facilitates market analysis, servicing, recalls, etc.

In some embodiments, objects that include dendritic structures can beidentified. Methods for performing such identification can includereading the dendritic structure to provide a signal, generating a uniqueidentifier from the signal, and identifying the object using the uniqueidentifier. Anti-counterfeiting measures for high value objects,including banknotes, high-end goods, and critical components, frequentlyinvolve the use of complex optical patterns or the addition of hard tocopy images such as holograms. The main problem with these approaches isthat the patterns are the same for multiple items and so there is aneconomic justification for the effort to reproduce them in largequantities (e.g., banknote forgery is extremely difficult and expensivebut is clearly worthwhile if large numbers of counterfeit bills areinvolved). A unique and unobtrusive authentication code for each suchitem would help to prevent mass counterfeiting as not only would everyitem have to have a different code, making duplication more difficult,but the code could also be maintained in a database that would be usedto confirm authenticity and also track the objects. For example, readingcan be performed using a commonly available device such as a smartphone,connected via the Internet to a central database and having a customattachment to allow high numerical aperture optical scanning or electricreading, so that a purchaser, retailer, or police officer could performon-the-spot authentication.

The use of dendritic structures as unique “fingerprints” is mosteffective when dendritic structures are difficult to copy. As discussedpreviously, the dendritic structure fabrication methods disclosed hereinnot only produce unique, extremely small two-dimensional dendriticstructures, but the structures also feature a complex surface with manyfacets on the electrodeposit. This 3D pattern is very difficult toreproduce accurately at reasonable cost and so the economic impetus forcopying single dendritic structures is greatly reduced.

In some embodiments, a dendritic structure that includes multipleelements can be read using the above techniques and also analyzed usinga materials analysis technique, such as x-ray fluorescence, to determineits composition. This “compositional coding” provides an extra layer ofsecurity as it makes counterfeiting the dendritic structure verydifficult.

Anti-counterfeiting technologies in semiconductors currently involvecustom silicon cores that are added to custom/application specificintegrated circuits (ASICs) or placed in a system as a stand-alone chip.These cores are complicated, consume additional power, and addsignificant area/cost to the ASIC or circuit board. The dendriticstructures described herein are simple passive devices that can be addedto any circuit with little area penalty and operated at extremely lowpower to produce a unique digital identifier for each chip. In addition,the structures can be generated in-situ either during manufacture(testing/assembly) or by the user in the field and can also beregenerated multiple times in service. The fabrication methods alsoproduce no external cues; embedded dendritic structures cannot be readby analyzing the chip power consumption or electromagnetic emissions.The dendritic structures can be destroyed by applying a burst ofelectrical energy from, for example, a battery or supercapacitor in theevent that the system containing the structure is tampered with. Thisallows the structure and the information it represents to be kept out ofthe hands of those who should not have access to it.

Anti-counterfeiting measures for non-electronic objects, includingbanknotes and high-end goods, typically involve the use of complexoptical patterns or the addition of hard to copy images such asholograms. The dendritic structure fabrication methods disclosed hereinnot only produce unique two-dimensional structures, but each structurealso has a complex surface with many reflective facets on theelectrodeposit. Fabricating a structure that would accurately reproducethe 3D light scattering pattern from a dendritic structure is verydifficult, and therefore the use of dendritic structures asanti-counterfeiting measures has important advantages over conventionalmeasures.

In some embodiments, data can be encrypted using information derivedfrom dendritic structures. A dendritic structure can be read to providea signal, and a unique identifier is generated from the signal and usedas a key in the encryption of the data. Encryption of data for securityduring transmission or storage typically involves an encryption keywhich specifies how the message is to be encoded. An authorized party isable to decode the encrypted data using an algorithm that requires adecryption key that eavesdroppers do not have access to. Conventionalencryption schemes typically use a key-generation algorithm to randomlyproduce keys. True random number generation is generally difficult andtypically involves complex algorithms. The simplicity of the fabricationmethods disclosed herein and the random resulting dendriticstructures—with only voltage and time as inputs to the fabricationprocess—is a significant advantage over current methods of random numbergeneration. Since the dendritic structure and therefore the numericalkey can be generated inside an integrated circuit during or aftermanufacture, the use of dendritic structures for data encryption can besimpler and more secure than other key generation methods. In certainembodiments, the key generator can also be used to provide a digitalsignature for authentication of information.

Certain features and aspects of particular applications of the dendriticstructures disclosed herein have been described above. These and otherapplications will be described in greater detail in subsequent sectionsof this disclosure.

The fabrication methods disclosed herein typically yield, in astraightforward manner, a random identifier (e.g., dendritic structure)via the application of a small voltage to a simple fabricationapparatus. Existing technologies typically either involve complexelectronics and algorithms to produce unique and/or random numbers orpatterns. Both the apparatus and the method of generating the dendriticstructures are simple and can be performed at low cost. The powerconsumption in programming and reading the fabricated structures is alsovery modest.

The following describes one example of fabrication of a dendritic metalstructure. On a layer of perylene, Ge₃₀Se₇₀ base glass (2400 Å thick)and silver layers (800 Å thick) were thermally evaporated and patternedon the diaphragm. The ratio of Ge₃₀Se₇₀ to Ag was approximately 3:1Immediately after the deposition, photo-dissolution was performed usinga 15 min UV exposure to diffuse silver into the Ge₃₀Se₇₀ layer to formthe solid electrolyte. The anode (silver) and cathode (nickel) wereseparately evaporated and patterned on the diaphragm. A voltage bias wasthen applied across the anode and the cathode to grow a dendritic metalstructure.

As another fabrication example, a 50 nm layer ofGe_(0.20-0.04)Se_(0.80-0.60) was first deposited onto the surface of apolysilicon material, and the Ge—Se layer was covered with about 20 nmof silver. The silver was dissolved into the Ge—Se glass by exposing thesilver to a light source having a wavelength of about 405 nm and a powerdensity of about 5 mW/cm² for about ten minutes. Any excess silver wasthen removed using a Fe(NO₃)₃ solution. The solid electrolyte materialwas then patterned and etched to provide a desired shape.

A DC bias from 3 to 10 V was applied to electrochemically grow adendritic silver structure extending out from the tip of the cathode,which is shown in FIG. 2. FIG. 3 shows a SEM micrograph of theelectrodeposited dendritic silver structure. A VEECO NT9800 opticalprofilometer was used to measure the optical profile in FIG. 3, whichshows that the dendritic silver structures had a height on the order of90 nm.

A further fabrication example is shown in FIGS. 10A and 10B. A cathodeand a silver anode were deposited on the surface of a solar cell, and alayer of water was disposed thereon, as shown in the image of FIG. 10A.Dendritic structures were fabricated by applying a 20 V bias across theelectrodes for 10 minutes. The dendritic structures are shown in theimage of FIG. 10B. Dendritic structure growth was also observed on SiO₂layers, at an applied bias voltage of 5 V for 10 minutes.

Volume Fabrication of Dendritic Structures

As discussed above in connection with FIG. 1, the anode(s) used in thefabrication of dendritic structures is/are typically formed from a metalsuch as copper, silver, or an alloy of copper and/or silver. Thecathode(s) is/are typically formed from any one or more of a variety ofelectrically conductive materials, such as aluminum, tungsten, nickel,molybdenum, platinum, gold, chromium, palladium, metal silicides, metalnitrides, and/or doped silicon. An electrolyte in the form of a liquidcan be deposited atop a substrate so that both the cathode and the anodeare positioned within the volume of liquid. The liquid can include, forexample, water, or another liquid in which metal cations are soluble.More generally, the electrolyte can include a variety of substances,including gels and solid films, in which metal cations are labile.

The cathode and anode are in electrical contact with the liquid byvirtue of their positions within the liquid. Accordingly, when anelectrical potential difference is applied between the cathode and theanode, a dendritic structure begins to grow in a general direction fromthe cathode to the anode. The dendritic structure is generally formedfrom the metal (or one of the metals) that form(s) the anode. Duringdeposition of the dendritic structure, metal cations in the electrolyteare reduced at the cathode, and extend the dendritic structure in thedirection of the anode. In some embodiments, metal atoms of the anodeare oxidized to form cations during deposition of the dendriticstructure. The cations dissolve in the electrolyte (e.g., a liquid) toreplace the reduced cations that form the dendritic structure. Incertain embodiments, the anode is not oxidized, and the dendriticstructure is formed only from metal cations dissolved in the liquid whenthe liquid is deposited on the substrate.

The morphology of a particular dendritic structure will generally dependupon a number of factors, including the geometry of the cathode andanode, the metal cations that form the dendritic structure, thepotential difference applied between the cathode and anode, the ioniccurrent between the cathode and anode, the nature of the electrolyteacting as the ion transport medium, and the deposition time. In general,dendritic structures can be formed from a variety of metals including,but not limited to, silver, copper, zinc, gold, iron, tin, and mixturesthereof.

The fabrication methods described so far can readily be used tofabricate a variety of dendritic structures. However, use of dendriticstructures for large volume commercial applications and transactionsrequires that the structures be fabricated in large numbers. The methodsdisclosed to this point are suitable for relatively low-volumefabrication of dendritic structures. In this section, additional methodsare disclosed for fabricating larger numbers of dendritic structures.

FIGS. 11A and 11B illustrate schematically a batch fabrication methodfor forming dendritic structures on a substrate. In FIG. 11A, a cathode1310 that includes a plurality of cathode probes 1312 arranged in anarray structure is positioned in contact with a substrate 1314 immersedin an electrolyte bath 1316. Positioned on the opposite side ofsubstrate 1314 from cathode 1310 is an anode 1318.

With cathode 1310 and anode 1318 positioned as shown in FIG. 11A, anelectrical potential difference is applied between the cathode andanode. As a result of the potential difference, metal cations dissolvedin electrolyte bath 1315 are reduced at the tips of each of cathodeprobes 1312 where the tips contact substrate 1314. At the position ofeach probe tip on substrate 1314, a dendritic structure grows radiallyoutward in the plane of substrate 1314. In this manner, an array ofradial dendritic structures is formed on the surface of substrate 1314,where the positions of the dendritic structures match the positions ofthe tips of cathode probes 1312 in contact with substrate 1314. After aselected time interval has elapsed during which the potential differenceis applied between cathode 1310 and anode 1318, the applied potentialdifference is removed and cathode 1310 is lifted relative to substrate1314, yielding a substrate with an array of dendritic structures 1320formed thereon, as shown in FIG. 11B.

In general, cathode 1310 and cathode probes 1312 are formed from arelatively inert, conductive material. In some embodiments, for example,cathode 1310 and/or cathode probes 1312 can be formed from one or moremetals. In certain embodiments, cathode 1310 and/or cathode probes 1312can be formed from one or more semiconductor or ceramic materials.Examples of materials that can be used to form cathode 1310 and/orcathode probes 1312 include, but are not limited to, aluminum, tungsten,nickel, molybdenum, platinum, gold, chromium, palladium, metalsilicides, metal nitrides, and/or doped silicon.

Cathode probes 1312 are typically extended structures arrayed in apattern in cathode 1310. In some embodiments, the shapes of cathodeprobes 1312 can influence the geometrical properties of dendriticstructures 1320 that are deposited from the tips of the probes, due tothe manner in which the geometrical shapes of cathode probes 1312influence the rate of reduction of metal cations at the probe tips. Insome embodiments, for example, cathode probes 1312 are needle-like inshape (e.g., the cross-sectional area of probes 1312 is approximatelyconstant along their width). In certain embodiments, cathode probes 1312are conical in shape, with a cross-sectional area that varies alongtheir length. In general, however, cathode probes 1312 have a relativelylarge aspect ratio, which is defined herein the ratio of the length of aprobe (e.g., measured in a direction parallel to a central axis of theprobe) to its maximum cross-sectional area. For example, the averageaspect ratio for cathode probes 312 in cathode 310 can be 2:1 or more(e.g., 3:1 or more, 4:1 or more, 5:1 or more, 7:1 or more, 10:1 or more,15:1 or more).

Although cathode probes 1312 are shown as forming a square orrectangular array in cathode 1310, more generally, cathode probes 312can be positioned in any regular or irregular geometry in cathode 1310.In some embodiments, for example, cathode probes 1312 can be positionedto form a hexagonal array. In certain embodiments, cathode probes 1312can be positioned to form a circular array and/or a radial array. Morecomplex patterns of cathode probes 1312 (e.g., patterns featuring two ormore different arrays, and/or patterns with different spacings betweencathode probes 1312 in different rows, columns, or portions of thepattern) can also be used. In general, different patterns can be usedaccording to the particular morphology of the dendritic structures thatare deposited. For example, for dendritic structures that exhibitasymmetrical growth patterns, cathode probes 1312 arranged so thatspacings between the probes are not uniform in all directions can beused.

Various methods can be used to fabricate an array of cathode probes1312. In some embodiments, a probe array can be formed by attachingadjustable rigid or spring-loaded probes to a rigid conducting baseplate so that all of the probes are electrically connected, forming acommon cathode. In certain embodiments, groups of one or more probes canbe connected to individual conducting tracks on a base plate. FIG. 39shows an embodiment of a cathode 1310 that includes a plurality ofconducting tracks 1311, each of which is electrically isolated from theother conducting tracks. Conducting probes 1312 are each connected toone of the conducting tracks. Individual electrical potentials can beapplied to each of the conducting tracks 1311. For example, differentpotentials can be applied to some of tracks 1311 to ensure that uniformgrowth of dendritic structures occurs across cathode 1310.

In the methods disclosed above, a variety of different materials can beused to form substrate 1314. Typically, substrate 1314 is formed of amaterial that is sufficiently rigid mechanically to support dendriticstructures 1320, but is also sufficiently compliant so that it can beprocessed later to separate individual dendritic structures. In someembodiments, for example, substrate 1314 is formed of one or moreplastics, such as polyethylene (e.g., polyethylene terephthalate, PET),polypropylene, polyester, polystyrene, polyamide, polyolefin, acetate,acrylate, vinyl, polyester, Mylar®, Teflon®, and/or Teslin®. In certainembodiments, substrate 1314 is formed of paper-based materials, such asplasticized paper.

Anode 1318 generally includes the material(s) from which dendriticstructures 1320 are formed. For example, in some embodiments, dendriticstructures 1320 are formed from (or include) silver, and anode 1318 islikewise formed from (or includes) silver. In certain embodiments,dendritic structures 1320 are formed from (or include) copper, and anode1318 is likewise formed from (or includes) copper. More generally,dendritic structures 1320 can be formed from one or more metals, andanode 1318 can include some or all of the one or more metals, and canalso include additional materials, such as additional metals, as well.Anode 1318 can include a variety of other materials. In someembodiments, for example, anode 1318 can include one or more relativelyinert materials to reduce or prevent undesirable side-reactions (e.g.,sulfide formation) from occurring at the anode and/or to promote uniformerosion of anode 1318 during oxidation of the active metal in the anode.For example, metals such as palladium can be included in anode 1318.

Anode 1318 can generally have a variety of shapes. Typically, anode 1318is shaped to ensure that the electric field across substrate 1314 isspatially uniform to ensure uniform growth of dendritic structures onthe substrate.

Electrolyte bath 1316 generally includes dissolved ions of the one ormore materials from which dendritic structures 1320 are formed. Forexample, where dendritic structures 1320 are formed from one or moremetals, electrolyte bath 1316 includes dissolved cations of the one ormore metals. As explained above, when a potential difference is appliedbetween cathode 1310 and anode 1318, cations dissolved in electrolytebath 1316 are reduced at the tips of cathode probes 1312, resulting inthe growth of dendritic structures 1320 on substrate 1314 at positionswhere the tips of cathode probes 1312 contact substrate 1314. Atoms ofanode 1318 are oxidized by the applied potential difference to formcations, which then dissolve in electrolyte bath 1316, replenishing thecations that were reduced.

In addition to cations of the materials that form dendritic structures1320, electrolyte bath 1316 includes one or more solvents. The solventscan be in liquid form, such as water and/or other polar liquids. In someembodiments, the solvents can be in the form of gels, such aswater-based gels and/or other gels. Examples of gels that can be used inelectrolyte bath 1316 to solvate cations for forming dendriticstructures 1320 include, but are not limited to, silver nitrate orcopper sulfate in cellulose, polymethylmethacrylate, polyacrylamide,and/or polyvinylidene fluoride. Solid electrolytes that can be used inthin film form include, but are not limited to, crystalline silverhalides (e.g., AgI) and silver chalcogenides (e.g., Ag₂S, Ag₂Se, andAg₂Te), and their copper counterparts, and As_(x)S_(1-x)—Ag,Ge_(x)Se_(1-x)—Ag, Ge_(x)Si_(1-x)—Ag, As_(x)S_(1-x)—Cu,Ge_(x)Se_(1-x)—Cu, Ge_(x)S_(1-x)—Cu, where x ranges from about 0.1 toabout 0.5, other chalcogenide materials incorporating silver, copper,zinc, iron, and combinations of these materials, Ag- and Cu-dopedtransition metal oxides, and Ag- and Cu-doped silicon or germaniumoxides.

As discussed above, an electrical potential is applied between cathode1310 and anode 1318 to grow dendritic structures on substrate 1314.Voltages that are applied are typically 100 mV or more (e.g., 200 mV ormore, 300 mV or more, 500 mV or more, 700 mV or more, 900 mV or more)and/or 100 V or less (e.g., 80 V or less, 60 V or less, 40 V or less, 30V or less, 20 V or less, 10 V or less). The magnitude of the appliedelectrical potential is generally selected to control the growth rateand/or growth morphology of the dendritic structures on substrate 1314.The growth duration typically ranges from 1 s or more (e.g., 2 s ormore, 4 s or more, 6 s or more, 8 s or more) to 60 s or less (e.g., 50 sor less, 40 s or less, 30 s or less, 20 s or less).

Dendritic structures 1320 used for the applications that will bediscussed subsequently are typically relatively small. For example,dendritic structures 1320 can have a maximum dimension measured in theplane of substrate 1314 of about 2 mm or less. Accordingly, dendriticstructures 1320 are relatively delicate. If the structures depositedadhere to the tips of cathode probes 1312 when the probes are liftedfrom the surface of substrate 1314, dendritic structures 1320 can besignificantly disrupted, and may even be destroyed.

To avoid damaging dendritic structures 1320 in this manner, variousmethods can be used to reduce the likelihood that dendritic structures1320 will adhere to the tips of cathode probes 1312. In someembodiments, for example, the surfaces of cathode probes 1312 can becoated in a material that reduces such adherence. Examples of materialsthat can be used for this purpose include, but are not limited to,conductive liquids such as various oils, and conducting solids such asgraphite.

In addition, or as an alternative, in some embodiments, dendriticstructures 1320 can be deposited on the side of substrate 1314 oppositeto cathode 1310. FIG. 12 shows a schematic diagram illustrating suchmethods. In FIG. 12, a cathode 1310 that includes a plurality of cathodeprobes 1312 is positioned so that the tips of cathode probes 1312 piercesubstrate 1314, which is positioned in an electrolyte bath 1316 suchthat the upper surface of substrate 1314 (i.e., the surface closest tocathode 1310) does not contact the electrolyte bath. Anode 1318 is alsoin contact with electrolyte bath 1316.

As shown in FIG. 12, the tips of cathode probes 1312 extend throughsubstrate 1314 to the underside of the substrate (i.e., the side ofsubstrate 1314 closest to anode 1318, and opposite to the side on whichcathode 1310 is nominally positioned. When a potential difference isapplied between cathode 1310 and anode 1318, electrodeposition ofdendritic structures 1320 occurs at the tips of cathode probes 1312, asdescribed above. However, because the tips of cathode probes 1312 arepositioned on the underside surface of substrate 1314 as shown in FIG.12, dendritic structures 1320 are electrodeposited on the undersidesurface of the substrate. After deposition is complete (i.e., after thedeposition time has elapsed), cathode 1310 is lifted away from substrate1314, withdrawing cathode probes 1312 from the substrate. As cathodeprobes 1312 are lifted, however, dendritic structures 1320 remainpositioned on the underside surface of substrate 1314. Using thistechnique, damage to the fragile dendritic structures can besignificantly mitigated or eliminated.

In FIGS. 11A and 11B, an array of cathode probes 1312 is arranged oncathode 1310 to form a corresponding array of radial dendriticstructures 1320 on the surface of substrate 1314. More generally,however, the cathode probes 1312 can be positioned to fabricate largenumbers of dendritic structures 1320 with a variety of shapes.

For example, in some embodiments, the cathode can include a plurality ofcathode probes arranged to fabricate parallel dendritic structures. FIG.13 is a schematic diagram illustrating a method for forming dendriticstructures that extend in approximately parallel directions with respectto one another. In FIG. 13, a cathode 1410 featuring a one-dimensionalarray of cathode probes 1412 is positioned within an electrolyte bath1416 so that the cathode probes are in contact with a substrate 1414.Also positioned within bath 1416 is an anode 1418. When an electricalpotential difference is applied between cathode 1410 and anode 1418,dendritic structures 1420 grow approximately along the directionindicated by arrow 1422. In general, in the method shown in FIG. 13, thefeatures of cathode 1410, cathode probes 1412, substrate 1414,electrolyte bath 1416, and anode 1418 are similar to the featuresdisclosed in connection with the corresponding components shown in FIGS.11A and 11B.

In some embodiments, dendritic structures are fabricated on non-planarsubstrates using the methods discussed above. FIG. 40 shows anembodiment of a substrate 1314 that includes a plurality of raisedstructures 1315. Dendritic structures 1320 are grown on the surfaces ofraised structures 1315. In some embodiments, a single dendriticstructure 1320 is grown on each raised structure 1315. Alternatively, incertain embodiments, multiple dendritic structures 1320 can be grown oneach raised structure 1315, so that the height of dendritic structures1320 above the planar portion of substrate 1314 will, in general, vary.

A variety of different patterned substrates 1314 can be used to supportdendritic structures 1320. In addition to patterns of raised structures1315 as shown in FIG. 40, substrates having surfaces that are scored,corrugated, curved, undulating, and include various combinations ofnon-planar features can function as growth surfaces for dendriticstructures. In addition, dendritic structures 1320 can be grown on avariety of substrates with curved surfaces. For example, dendriticstructures 1320 can be grown on a cylindrical or spherical surface of asubstrate 1314.

Using a non-planar substrate 1314 can provide a number of advantages.For example, when dendritic structures 1320 are grown on a non-planarsubstrate 1314, the dendritic structures conform—at least to someextent—to the shape of the substrate. As a result, duplicatingparticular dendritic structures is made more difficult. Further, certainprinting methods are not capable of producing dendritic structures on anon-planar substrate, thus foreclosing these methods from replicatingthe dendritic structures.

Further, in some embodiments, the non-planar features of substrate 1314(e.g., raised structures 1315 in FIG. 40) can be used to preventtampering with the dendritic structures. For example, raised structures1315 can be filled with a mildly corrosive material (e.g., a mild acidor base). If tampering with the fabricated dendritic structures 1320occurs, the corrosive material is liberated from raised structures 1315and erodes dendritic structures 1320, rendering them unsuitable forauthentication or other applications. In this manner, improper transferof the dendritic structures from one article to another can beprevented. Additional methods for preventing tampering with dendriticstructures will be discussed subsequently.

In addition, in certain embodiments, raised structures 1315 filled witha mildly corrosive material can be used to fabricate time-limited (e.g.,expiring) dendritic structures. In particular, raised structures 1315can be fabricated from a material that is at least partially porous to,or eroded by, the corrosive material so that over time, the corrosivematerial penetrates through structures 1315 and erodes dendriticstructures 1320. Once eroded, dendritic structures cannot be used forauthentication or other applications. In this manner, time-limited, orexpiring, dendritic structures (e.g., where the time limit is determinedby the rate at which dendritic structures 1320 are eroded by thecorrosive material in raised structures 1315) can be fabricated.

The foregoing methods for large-volume fabrication of dendriticstructures may collectively be thought of as batch methods, as theyinvolve forming multiple dendritic structures on a common substrateduring a common growth period. Other methods can also be used forlarge-volume fabrication of dendritic structures. For example, a varietyof continuous, roll-to-roll methods can also be used.

FIG. 14 is a schematic diagram illustrating an example of a method forcontinuous fabrication of dendritic structures. In FIG. 14, substrate1514 is provided in spool form, mounted on substrate feed roller 1522.Also shown in FIG. 14 are cathode 1510, implemented as a roller thatrotates in the direction shown by arrow 1530. Cathode 1510 includes aplurality of cathode probes 1512 that extend radially outward from thecathode.

Cathode 1510 is positioned partially immersed in electrolyte bath 1516.Anode 1518 forms a vessel that contacts and contains electrolyte bath1516.

Substrate 1514 is threaded over guide roller 1532, around cathode roller1510 and through electrolyte bath 1516, over guide roller 1534, and ontoproduct roller 1524. To fabricate dendritic structures on substrate1514, the substrate is translated in the direction shown by arrows 1526and 1528, e.g., by activating product roller 1524 to draw substrate 1514from substrate feed roller 1522 over guide roller 1532, around cathode1510 and through electrolytic bath 1516, over guide roller 1534, andonto product roller 1524. When each portion of substrate 1514 passesthrough electrolyte bath 1516, a potential difference is applied betweencathode 1510 and anode 1518. Cathode probes 1512 contact the surface ofsubstrate 1514. Dendritic structures grow radially on the surface ofsubstrate 1514 at positions where cathode probes 1512 contact thesubstrate. In general, the features associated with the cathodes,anodes, substrates, and electrolyte baths described above also apply tothe components shown in FIG. 14.

In FIG. 14, substrate 1514 is typically fed continuously throughelectrolyte bath 1516. However, in some embodiments, substrate 1514 canbe fed in a step-wise manner through the electrolyte bath, e.g.,depending on the ease with which dendritic structures grow on a movingsubstrate. Typically, portions of substrate 1514 remain immersed inelectrolyte bath 1516 for a period of time from a few seconds (e.g., 2seconds or more, 5 seconds or more, 10 seconds or more, 20 seconds ormore) to a few hundred seconds (e.g., 900 seconds or less, 800 secondsor less, 600 seconds or less, 400 seconds or less, 300 seconds or less,200 seconds or less, 100 seconds or less).

In some embodiments, substrate 1514 can be co-rolled with one or moreadditional materials on product roller 1524 to reduce or prevent damageto the dendritic structures. Materials that are suitable for co-rollingwith substrate 1514 include the various materials disclosed herein thatare used for encapsulating dendritic structures.

As discussed in connection with FIG. 12, in some embodiments, thedendritic structures can be grown on the underside of substrate 1514(e.g., the side of substrate 1514 closest to anode 1518) to make iteasier to separate the delicate structures from cathode probes 1512. Inthe method shown in FIG. 14, the tension maintained in substrate 1514 byproduct roller 1524 and feed roller 1522 can be used to ensure thatcathode probes 1512 penetrate through substrate 1514 and rest on theunderside surface of the substrate. Once the dendritic structures aregrown on the underside of substrate 1514, cathode probes 1512 arewithdrawn from the substrate by the rotational motion of cathode 1510,leaving intact dendritic structures on the substrate.

The tension maintained in substrate 1514 by product roller 1524 and feedroller 1522 has the added benefit of ensuring close contact between theupper surface of substrate 1514 and cathode 1510, so that electrolytebath 1516 does not contact the upper surface of substrate 1514. As aresult, dendritic structure growth is confined to the underside surfaceof substrate 1514.

In some embodiments, to grow dendritic structures on the upper surfaceof substrate 1514 (e.g., the surface closest to cathode 1510), spacerscan be used to ensure that cathode probes 1512 contact the upper surfacerather than penetrating the substrate through to the lower surface. FIG.15 shows a schematic diagram of an embodiment of cathode 1510, in whichspacers 1536 are positioned on the surface of the cathode so thatcathode probes 1512 do not penetrate through substrate 1514, and insteadonly contact the upper surface of substrate 1514. Alternatively, or inaddition, spacers can be positioned directly on cathode probes 1512 toensure that the probes contact only the upper surface of substrate 1514.In general, spacers positioned on the surface of cathode 1510 and/or oncathode probes 1512 can be formed from a variety of materials. Examplesof suitable materials include, but are not limited to, ceramics,polymers, and inert metals.

The methods shown in FIGS. 11A, 11B, and 12-14 involve the growth ofdendritic structures in electrolyte baths. However, large-volumefabrication methods for dendritic structures that do not involveelectrolyte baths can also be used. In particular, substrates can bepre-coated or pre-immersed in an electrolyte to enable dendritic growthwithout using an electrolyte bath. FIG. 16A is a schematic diagram of asubstrate 1614 that supports the growth of dendritic structures.Substrate 1614 includes a base layer 1640 formed from one or more of thematerials disclosed previously for substrate 1314. Substrate 1614 alsoincludes an electrolyte layer 1638. In some embodiments, electrolytelayer 1638 can include one or more thin, solid films formed on baselayer 1640. Suitable materials for forming such a film include, but arenot limited to, any of the materials disclosed previously in connectionwith solid electrolytes. In certain embodiments, electrolyte layer 1638can include one or more gel layers applied to base layer 1640. Suitablegel materials include, but are not limited to, any of the materialsdisclosed previously in connection with gel-based electrolytes. In someembodiments, electrolyte layer 1638 can include a porous sheet (e.g.,formed of a material such as paper) that includes (e.g., is infusedwith) a liquid electrolyte material. Suitable liquid electrolytesinclude any of the electrolyte solutions disclosed previously.

Substrate 1614 is generally compatible with the fabrication methodsdiscussed previously. Thus, for example, substrate 1614 can be used tosupport the growth of dendritic structures via immersion baths, as shownin FIGS. 11A, 11B, and 12, and also via continuous fabrication methodsas shown in FIG. 14. Growth of the dendritic structures can occur oneither the upper or lower surface of substrate 1614.

In FIG. 16A, substrate 1614 includes an electrolyte layer 1638. In someembodiments, substrate 1614 can be pre-immersed in an electrolytesolution in addition to, or as an alternative to, the inclusion ofelectrolyte layer 1638. Immersing the substrate in an electrolytesolution infuses the substrate with metal cations that are subsequentlyreduced at the cathode to grow dendritic structures. In general, avariety of different electrolyte solutions can be used for immersion ofsubstrate 1614, including any of the solutions corresponding to theelectrolyte baths discussed above. Moreover, a variety of substratematerials are effective at absorbing electrolyte solutions, including,but not limited to, a variety of porous materials such as differentpaper-based materials.

High quality dendritic structures have been successfully grown on avariety of paper-based materials. Various methods can be used tofabricate dendritic structures on paper. In some embodiments, forexample, a paper substrate (e.g., laboratory filter paper) is soaked inan electrolyte solution. While any of the electrolyte materialsdisclosed herein can be used to immerse the paper substrate, silvernitrate solutions have been found to yield good results. Theconcentration of the solution used is typically larger than 0.01 M,e.g., between 0.1 M and 1.0 M. A silver nitrate solution at aconcentration of 0.1 M has been found to yield good results.

After the paper has been soaked, a cathode is positioned on the paperwhere the dendritic structure will be grown. Dendritic structures can befabricated on the paper without applying an anode, since the metal ionsthat form the dendritic structure are present in the electrolytesolution taken up by the paper substrate. However, in certainembodiments, an anode can be positioned at another location (e.g.,different from the cathode location) on the electrolyte-soaked paper.

Next, an electrical potential difference is applied between the cathodeand the electrolyte in the paper or the anode (if the anode is present).Typically, a potential difference of approximately 10 V is applied for afew tens of seconds (e.g., between 10 s and 60 s) to grow the dendriticstructure at the position of the cathode on the paper substrate.Following growth of the dendritic structure, the cathode (and anode, ifpresent) are removed from the paper substrate, and the paper is dried.

Using paper-based substrates provides a number of important advantages.Paper is a low-cost material that is available in large quantities and avariety of different forms (e.g., compositions, textures, strengths). Asa result, the nature of the paper selected for the substrate can bechosen based on the intended application; for example, stronger papersubstrates can be selected for applications that are anticipated toinvolve more frequent mechanical handling of the dendritic structures.

Dendritic structures have also been observed to adhere well topaper-based substrates. Without wishing to be bound by theory, theobserved adherence may be due to the relatively rough surface of paperat the microscopic level. As papers with a wide variety of differenttextures can be used as substrates, adherence of the fabricateddendritic structure to the substrate can therefore be selected based onthe choice of paper used for the substrate.

In addition, paper-based materials are typically porous and as a result,a variety of different electrolyte materials can be introduced intopaper-based substrates using techniques such as immersion (e.g.,soaking), as described above. Introducing electrolyte materials directlyinto the substrate significantly simplifies the growth process for thedendritic structures. Moreover, as described above, in some embodimentsdendritic structures can even be grown without using an anode.

The methods disclosed herein for fabricating dendritic structuresdirectly on paper-based substrates enable the use of dendriticstructures as security-related elements in a variety of importantsecurity-related applications. Many financial, legal, and identificationdocuments are printed on paper, and are therefore subject to possibleduplication and/or forging. More generally, a wide variety of controlleddocuments (e.g., documents over which security access restrictions areimposed, including secret papers, plans, blueprints, etc.) are printedon paper. Using the methods disclosed herein, dendritic structures canbe fabricated directly on such documents using low-cost, rapidprocessing techniques. Further, using methods that are described ingreater detail subsequently, the dendritic structures can beauthenticated, and then used to identify the documents on which they aregrown. The strong adherence of the dendritic structures to paper-basedsubstrates makes removal of the dendritic structures from the documentsdifficult. Mechanical and/or chemical methods for removal, for example,are likely to lead to destruction of the dendritic structures,preventing identification of the documents on which they are grown. Inthis manner, dendritic structures can be used to identify and secure awide variety of documents that would otherwise be subject tocounterfeiting efforts. Examples of such documents include, but are notlimited to, banknotes, cheques, bearer bonds, stock certificates, wills,contracts, deeds, passports, birth certificates, and licenses of varyingtypes (e.g., driver's licenses).

In addition to paper-based substrates, a variety of porous substratescan be used for the fabrication of dendritic structures using techniquessimilar to those disclosed above. In fabrication methods involving suchsubstrates, an electrolyte (e.g., a liquid, gel, or paste electrolyte)is applied to the substrate material by immersion, spraying, contactdeposition, or a direct mechanical application. A cathode is applied tothe substrate surface and electrolyte and, optionally, an anode can alsobe applied. An electrical potential difference is applied between thecathode and the electrolyte in the porous material (or the anode, ifpresent) to grow the dendritic structure. Using such methods, thefabricated dendritic structures adhere very strongly to the poroussubstrate. Without wishing to be bound by theory, it is believed thatthe strong adhesion occurs because the dendritic structures at leastpartially form in the pores or gaps of the substrate material, whichphysically “locks” the dendritic structures in place on the substratesurface. The foregoing fabrication methods are therefore particularlywell suited to prevention of tampering with the dendritic structures, asthe physical adhesion and “locking” of the structures to the poroussubstrate makes mechanical or chemical removal of the structures fromthe substrate—without damaging the structures—very difficult.

As described above, when the electrolyte material (e.g., liquid, paste,or gel) has an ionic concentration that is sufficiently large(typically, greater than 0.01 M), and the electrolyte material is“sacrificial” (e.g., it is not retained after growth for subsequentfabrication of additional dendritic structures), the dendriticstructures can be grown without an oxidizable anode that includes thesame material (e.g., metal atoms) from which the dendritic structuresare fabricated. Instead, the material used to form the dendriticstructures can be supplied by the electrolyte. Fabricating dendriticstructures in this manner can be advantageous, as it permits a varietyof non-reactive (e.g., non-oxidizable) anode materials to be used.Examples of such materials include tungsten, stainless steel, andplatinum.

Where the electrolyte material is sacrificial, growth of the dendriticstructures can occur without using an anode, as discussed above. Wherethe electrolyte material is not sacrificial (e.g., when the electrolytematerial is used in the fabrication of multiple batches of dendriticstructures), replenishment of the metal ions in the electrolyte istypically needed following a growth batch. As discussed herein,replenishment can occur from an oxidizable anode. However, theoxidizable anode does not have to be in contact with the substrate onwhich the dendritic structures are grown. For example, a non-reactiveanode can be used to contact the growth region of the substrate, and anelectrical potential difference can be applied between the cathode andthe non-reactive anode to initiate growth of the dendritic structures. Asacrificial anode can be positioned away from the growth region butstill in contact with the electrolyte material to replenish the ions inthe electrolyte. In some embodiments, fabrication of dendriticstructures and subsequent processing on the fabricated structures areperformed more easily if the sacrificial anode does not contact thegrowth region of the substrate.

Substrate 1614 in FIG. 16A includes a plurality of anodes 1618 patternedon the substrate. In some embodiments, e.g., where electrolyte layer1638 includes a solid electrolyte material, anodes 1618 can be depositedas a patterned film on electrolyte layer 1638 using methods such asphysical and/or chemical vapor deposition. Anodes 1618 can be formedfrom any one or more of the materials disclosed previously in connectionwith anode 1318.

As shown in FIG. 16A, anodes 1618 can be deposited in a patterned filmthat includes a plurality of openings 1613. Contact between cathodeprobes 1612 and electrolyte layer 1638 occurs within openings 1613, andgrowth of the dendritic structures therefore occurs within the openingsas well. Although anodes 1618 are patterned on the side of substrate1614 on which contact with cathode probes 1612 occurs in FIG. 16A,anodes 1618 can also be patterned on the opposite side of substrate1614.

In some embodiments, anodes 1618 can be provided in the form of a metalplate with openings to allow contact between cathode probes 1612 and theelectrolyte material. Referring to FIG. 16A, anodes 1618 can beimplemented in the form of a plate (e.g., formed of a metal such ascopper, or any of the other anode materials disclosed herein), whereopenings 1613 with cross-sectional shapes that are circular, elliptical,square, rectangular, or other regular or irregular shapes allow thecathode probes access to electrolyte layer 1638. FIG. 16C shows aschematic diagram of an anode plate 1618 that includes a plurality ofopenings 1613. The plate can be placed in contact with electrolyte layer1638 prior to the growth of the dendritic structures, and removed fromlayer 1638 when growth of the structures is complete.

In certain embodiments, substrate 1614 does not include anodes 1618.Instead, one or more anodes 1618 can be provided separately fromsubstrate 1614 (e.g., as a separate electrode or electrodes thatcontacts substrate 1614 only during growth of dendritic structures).FIG. 16B shows an embodiment in which a substrate 1614 includes a baselayer 1640 and an electrolyte layer 1638 as discussed above. In FIG.16B, a plurality of cathode probes 1612 contact electrolyte layer 1638.Further, a plurality of anodes 1618, each of which is concentricallypositioned relative to a corresponding cathode probe 1612, also contactelectrolyte layer 1638. When an electrical potential is applied betweencathode probes 1612 and their corresponding anodes, dendritic structuresgrow at positions where cathode probes 1612 contact electrolyte layer.

Anodes 1618 can generally be implemented in a variety of differentgeometries. In FIG. 16B, anodes 1618 are shown as a plurality of hollowtubes or rings that are coaxial with cathode probes 1612. Othergeometries are also possible including, for example, flat rings, hollowprisms, and pluralities of needle-like probes that are arranged incircular or other regular geometries.

Coaxial ring or tube anodes, as shown in FIG. 16B, are particularlyuseful for simultaneously fabricating multiple radial dendriticstructures. The symmetry of such anodes typically yields radialdendritic structures with a high degree of radial symmetry. Moreover,ring and/or tube anodes shield each dendritic growth point (e.g., thepoint where cathode probe 1612 contacts electrolyte layer 1638) from theother growth points, yielding highly uniform dendritic structureformation across the substrate.

When dendritic structures are grown on a substrate material that hasbeen infused with the electrolyte material (e.g., a porous substrate towhich electrolyte material has been applied or introduced), the one ormore anodes 1618 can be on the same side of the substrate as, oropposite side from, cathode probes 1612. Where anodes 1618 arepositioned on the opposite side of the substrate from cathode probes1612, either the cathode probes 1612 or anodes 1618 can penetrate intothe substrate (e.g., into electrolyte layer 1638) to enhance the growthof the dendritic structures.

In some embodiments, electrolyte materials can be delivered by anodes1618, cathode probes 1612, or both the anodes and cathode probes, to thesubstrate during fabrication of the dendritic structures. For example,FIG. 16D shows a cross-sectional view of an anode plate 1618 thatincludes a plurality of openings 1613. A fluid channel 1615 is formed inplate 1618, and includes apertures in the sidewalls of each of theopenings 1613. The fluidic channel is connected to an electrolytereservoir 1617 via a tube 1619. During fabrication of dendriticstructures, fluid reservoir 1617 delivers electrolyte materials (e.g.,electrolyte solution) to each of the openings 1613 via fluid channel1615.

Electrolyte delivery can also be accomplished using other anodegeometries. For example, when anodes 1618 are implemented as a pluralityof rings or tubes, electrolyte materials can be delivered to thesubstrate surface through apertures formed in the rings or tubes. Therings or tubes can be connected to an electrolyte reservoir in a mannersimilar to FIG. 16D.

By implementing the anodes 1618 as a plurality of tubes, rings, orsimilar structures, or as a plurality of openings in a metal plate,anodes 1618 form a dendritic structure “print head” that can be rapidlypositioned and re-positioned on the surface of a substrate to facilitatehigh volume, high quality growth of dendritic structures. In someembodiments, anodes 1618 can also be used to cut substrate 1614 intoindividual pieces, each supporting a single fabricated dendriticstructure. For purposes of cutting substrate 1614, the edges of theanodes 1618 that contact substrate 1614 can be sharpened to penetratemore easily into the substrate material. Cutting substrate 1614 in thismanner can be highly advantageous, as the cutting process isautomatically aligned with the sites at which dendritic structures aregrown so that accurate sectioning of substrate 1614 can be achievedwithout performing any alignment steps.

When substrate 1614 includes an electrolyte layer or is pre-immersed inelectrolyte solution, the electrolyte material remains in placefollowing growth of the dendritic structures, unlike the methodsdisclosed in FIGS. 11A and 11B, for example, where the substrate isremoved from the electrolyte bath following growth of the dendriticstructures. In some embodiments, the composition of the electrolytelayer or electrolyte solution, the applied electrical potentialdifference, and/or the duration over which the potential difference isapplied, are adjusted so that the dendritic structures grown onsubstrate 1614 remain essentially stable (e.g., electrochemicallystable), even in the later presence of the electrolyte layer orelectrolyte solution.

Alternatively, in certain embodiments, the composition of theelectrolyte layer or electrolyte solution, the applied electricalpotential difference, and/or the duration over which the potentialdifference is applied, are adjusted so that during growth of thedendritic structures, the electrolyte layer or solution infused insubstrate 614 is starved of metal from the anode, i.e., the rate atwhich metal atoms from the anode are oxidized and dissolve in theelectrolyte layer or solution is insufficient to replace the metalcations that are reduced at the cathode. This can be achieved bylimiting the amount of metal in the anode to less than the amount in thedendritic structure so that the dendritic structure grows at the expenseof the metal ions in the electrolyte. The imbalance creates a chemicalgradient between the dendritic structure and the electrolyte followinggrowth, which will cause the dendritic structure to dissolve.

Following growth of the dendritic structures, the deficit of metalcations persists in the electrolyte layer or solution. Accordingly, theelectrolyte layer or solution slowly dissolves the fabricated dendriticstructures over a period of time, a process that is driventhermodynamically by the electrochemical and/or ionic imbalance in theelectrolyte layer or solution. Thus, by fabricating dendritic structuresin this manner, the structures can be made to “self-destruct” after aperiod of time. For structures that are used for identification orauthentication, as will be discussed later, the structures can thereforebe made to expire after a period of time. By adjusting the compositionof the electrolyte layer or electrolyte solution, the applied electricalpotential difference, and/or the duration over which the potentialdifference is applied, the expiration time of the fabricated dendriticstructures can be controlled. For example, by using an electrolyte layeror electrolyte solution that is closer to saturation with respect tocations from the anode, the longer it will take for the electrolytelayer or electrolyte solution to dissolve the dendritic structures. Theatomic percentage of metal in the electrolyte at saturation typicallyranges from 70 atomic percent to 10 atomic percent, depending in theelectrolyte; concentrations of metal cations smaller than the saturatedconcentration will cause gradual dissolution of the metal dendriticstructures.

In some embodiments, the dendritic structures can be further processed(e.g., during or after fabrication) to enhance their features, inparticular for imaging and/or packaging purposes. For example, one ormore additional materials can be deposited atop the dendritic structuresto “smooth” the structures for packaging purposes. Examples of suchmaterials include, but are not limited to, cyanoacrylate applied as alow viscosity (high-wicking) liquid and hardened by chemical reactionwith water or UV exposure to form a hard acrylic coating,polymethylmethacrylate liquid or vapor hardened by chemical reactionwith peroxide or UV exposure to form a hard Lucite® (Perspex®) coating,polyethylene terephthalate, polysiloxane liquid or condensed vapor thatis thermally cured to give a silicate coating, silicon dioxide orsilicon nitride deposited by the pyrolysis of vapor sources in achemical vapor deposition reaction to create a highly conformal oxide ornitride film. Polymeric materials such as polyvinylchloride andcellulose acetate may also be applied as a tape, affixed with adhesive,to cover the dendrite.

In certain embodiments, to enhance the visibility of reflections fromhigh points in the dendritic structures during imaging, the high pointsin the dendritic structures can be further “raised” above the surface ofthe substrate by applying an electric field during growth of thedendritic structures on the substrate. The field polarity is selected sothat metal cations are drawn upward relative to the substrate surfacedue to the influence of the field, which yield dendritic structures thatare more strongly peaked in a direction perpendicular to the substratesurface. Typical field strengths used for growing dendritic structuresin this manner are in a range from 10,000 to 1,000,000 V/cm.

In some embodiments, fluorophores can be attached to the dendriticstructures to produce light from the entire structure, which enhancesvisibility of the structures during image capture. Fluorophores can beattached over the entire dendritic structure, or attached selectively tocertain regions of the structure such as high points (e.g., which appearas peaks under illumination). Fluorophore attachment can be performed byattaching an ionic group to the fluorophore and applying a voltage ofthe opposite polarity to the dendritic structure so that the chargedfluorophores are particularly attracted to the regions of high electricfield at the peaks of the dendritic structure.

The methods discussed in this section generally yield a plurality ofdendritic structures fabricated in an ordered array on a substrate.Before the structures are used for various applications, however, avariety of additional processing steps can be performed. In FIG. 14, aprocessing station 1550 is positioned along the path of substrate 1514between guide roller 1534 and product roller 1524. More generallyprocessing station 1550 can be positioned at various points along thepath of substrate 1514 between feed roller 1522 and product roller 1524.In addition, in some embodiments, processing station 1550 can bepositioned after product roller 1524, i.e., processing station 1550 canbe positioned to process substrate 1514 after it has been spooled ontoroller 1524.

Processing stations can generally be present in any of the fabricationsystems disclosed herein. For example, the systems shown in FIGS. 11A,11B, and 12-16A/B can each include a processing station forpost-processing of fabricated dendritic structures. Each system can alsoinclude more than one processing station. For example, in someembodiments, similar processing stations can be used to processdendritic structures in parallel, thereby increasing the overallthroughput of the fabrication systems. In certain embodiments, multipleprocessing stations can be used to perform different post-processingsteps on the dendritic structures. These steps will be discussed furtherbelow. In general, the steps can be divided among any number ofpost-processing stations as desired.

FIG. 17 shows a schematic diagram of a post-processing station 1700 thatcan be used in any of the methods disclosed herein. Station 1700includes a drying module 1702, an inspection module featuring anillumination source 1704 and an imaging detector 1706, a marking module1708, a sealing module 1710, and a dicing module 1712. Substrate 1714with dendritic structures fabricated thereon passes through some or allof these modules.

Drying module 1702 functions to dry the fabricated dendritic structuresand substrate 1714 following growth. Drying module 1702 can beimplemented in a variety of ways. In some embodiments, for example,drying module 1702 features one or more sources configured to directflows of air (e.g., heated air) across the surface of substrate 1714. Incertain embodiments, drying module 1702 includes one or more radiativesources, such as infrared sources, that direct radiation onto substrate1714. The radiation heats substrate 1714 and can evaporate water andvolatile substances from the substrate. In some embodiments, conductiveand/or convective heating methods can be used in addition to, or asalternatives to, radiative heating. Further, heating methods thatinclude radio frequency waves (e.g., microwaves) can also be used.Typically, the curing temperatures for dendritic structures are between50° C. and 250° C.

The inspection module allows a system operator to view the fabricateddendritic structures and, for example, to designate certain dendriticstructures for rejection based on their morphology. In certainembodiments, an electronic processor 1716 coupled to illumination source1704 and imaging detector 1706 directs the light source to illuminatethe dendritic structures on substrate 1714, and directs the imagingdetector to obtain one or more images of the illuminated structures.Electronic processor 1716 then analyzes the images to the dendriticstructures and applies rejection criteria to determine whether specificstructures should be rejected. Dendritic structures can be rejectedaccording to a variety of criteria. For example, specific dendriticstructures can be rejected due to partial growth, a variety ofmorphological defects, and/or incorrect fractal dimension. Rejection canoccur immediately by ejecting specific dendritic structures from theprocessing sequence, or the dendritic structures can be marked for laterrejection. Rejection criteria can include, for example, the presence ofdefects that are larger than a threshold size (e.g., 0.1 mm), theabsence of particular branches in the dendritic structures, and afractal dimension that differs by 25% or more (e.g., 35% or more, 50% ormore, 75% or more) from a target value. The target value for dendriticstructures grown according to the methods disclosed herein is typicallyapproximately 1.5

Marking module 1708 applies marks, e.g., fiducial marks, to regions ofthe substrate. The marks can be used for subsequent processing steps,such as dicing substrate 1714. Alternatively, fiducial marks can beapplied so that the dendritic structures can be aligned for imaging,e.g., relative to a common reference position. Fiducial marks can beapplied using methods such as photolithography and etching of a film,laser etching, embossing, cutting, and/or drilling of the substrate.

In some embodiments, fiducial marks can be added to the substrate bytaking advantage of the photosensitivity of certain electrolytes in aphotolithographic process. For example, silver nitrate will darken whenexposed to light. Thus, a silver nitrate solution used as an electrolyteon a substrate can be exposed through a mask which contains a negativeimage of the fiducial pattern to create fiducial marks on the substrate.Exposure to create the fiducial marks can occur before or after growthof the dendritic structures.

Sealing module 1710 is configured to protect the fabricated dendriticstructures by applying one or more layers of protecting materials overthe dendritic structures. The protecting materials ensure that thedendritic structures are not subject to mechanical or chemicaldegradation during use. The protecting materials also are used to ensurethat the fabricated dendritic structures are not subject to tampering toalter their structure. This can be particularly important forapplications that involve identification and/or authentication, wherethe unique morphologies of specific dendritic structures are tied tospecific identity information. Methods for protecting the fabricateddendritic structures will be discussed in greater detail in a subsequentsection.

Dicing module 1712 is configured to slice substrate 1714 into multiplepieces to separate the dendritic structures. Typically, for example,substrate 1714 is diced so that each of the fabricated dendriticstructures is separated from the others. The dicing may be performedusing methods such as cutting/guillotining by a blade, sawing, lasercutting, or punching. The separated individual structures are then usedfor a variety of applications, examples of which are described herein.

Although post-processing station 1700 includes a drying module 1702, aninspection module featuring an illumination source 1704 and an imagingdetector 1706, a marking module 1708, a sealing module 1710, and adicing module 1712, more generally the post-processing stations caninclude all or only some of these modules. Further, the modules can bearranged in any order; post-processing station 1700 in FIG. 17 is onlyone example of a suitable arrangement. In some embodiments, for example,the inspection module can be positioned after all of the other modules,i.e., after the dendritic structures have been dried, protected, anddiced. Inspection can then proceed as described above to accept orreject the separated dendritic structures according to their specificmorphologies. In certain embodiments, drying module 1702 can bepositioned after sealing module 1710, particularly where sealing moduleapplies one or more layers to the dendritic structures that requiredrying following deposition.

Marking module 1708 can generally be positioned anywhere along theprocessing sequence. For example, in some embodiments, marking module1708 is positioned after dicing module 1712. Further, dicing module 1712can also typically be positioned anywhere along the processing sequence.In certain embodiments, such as the example shown in FIG. 14, substrate1714 can be fed directly into dicing module 1712 (e.g., a cuttingmachine) rather than onto product roller 1524, to separate individualdendritic structures.

FIG. 18 shows a specific dendritic structure 1820 that has been grownand post-processed, including having been diced to separate it fromother dendritic structures. Dendritic structure 1820 and the portion ofsubstrate that supports it form a dendritic tag 1800 that is circular inshape. More generally, however, dendritic tags can have a variety ofshapes, including square, rectangular, polygonal, elliptical, andvarious curved shapes. The maximum dimension of the dendritic tags,which is the largest distance between any two points on the dendritictags, is typically 5 mm or less (e.g., 4 mm or less, 3 mm or less, 2 mmor less, 1 mm or less).

Securing Dendritic Tags

Dendritic tags, fabricated as described in the preceding sections, haveunique morphological features that make them useful for a variety ofapplications, in particular, applications that involve identificationand authentication of articles. To be useful as unique identifiers,however, it is advantageous if the dendritic structures supported on thetags are difficult to tamper with following fabrication, and aresufficiently robust to retain their morphologies when exposed to avariety of physical and chemical environments. By rendering thedendritic structures difficult to modify or copy and the tags difficultto remove from articles to which they are applied, duplication or reuseof the tags for counterfeiting purposes is challenging and/oreconomically infeasible.

To prevent alteration of dendritic structure morphologies and to protectthe fabricated tags against degradation in a variety of differentenvironments, the present section discloses various systems and methodsfor treating fabricated dendritic structures. As discussed above inconnection with FIG. 17, these treatments can be applied to fabricateddendritic structures by sealing module 1710. Alternatively, or inaddition, the treatments can be applied using other means during orfollowing fabrication of the structures.

To protect dendritic tags against environmental degradation, one or morelayers of protective materials can be applied to encapsulate at leastthe tag's dendritic structure. FIG. 19 shows a schematic diagram of adendritic tag that includes a substrate 1914 and a dendritic structure1920 formed on the substrate. A protective layer 1902 is applied overdendritic structure 1920 to encapsulate the structure. Althoughprotective layer 1902 in applied to only one surface of substrate 1914in FIG. 19, more generally, protective layer 1902 can be applied to bothsurfaces of substrate 1914 to partially or fully encapsulate bothsubstrate 1914 and dendritic structure 1920. Further, although a singleprotective layer 1902 is applied to the dendritic tag, more generally,one or more protective layers can be applied. Multiple protective layerscan include different materials having different properties. Forexample, in some embodiments, a first protective layer can be applied tomechanical rigidity to the dendritic tag, and a second protective layercan be applied to impart water impermeability to the encapsulateddendritic tag. The following discussion will focus on properties ofprotective layer 1902 for clarity. However, it should be understood thata variety of different combinations of layers, each having differentproperties, can be used to protect dendritic tags. In particular,combinations of any number of layers of any of the different materialsdisclosed herein can be used.

In certain embodiments, protective layer 1902 has a relatively high Mohshardness number to resist mechanical abrasion of the encapsulateddendritic tag. In some embodiments, for example, the Mohs hardnessnumber of protective layer 1902 is 4 or more (e.g., 5 or more, 6 ormore, 7 or more, 8 or more). Further, in some embodiments, protectivelayer 1902 has relatively high water impermeability and degradesrelatively slowly in sunlight. These properties of protective layer 1902protect the encapsulated dendritic tag against environmentaldegradation.

In addition, in some embodiments, protective layer 1902 is relativelyresistant to a variety of different classes of chemical compounds,including some or all of acids, chlorine-based compounds, bleaches, anddetergents. The resistance of protective layer 1902 to these materialsfurther protects encapsulated dendritic tags.

Protective layer 1902 is generally applied to dendritic tags in a mannerthat preserves the delicate dendritic structure 1920 on each tag. Avariety of methods can be used for application of the protective layer.In some embodiments, for example, protective layer 1902 can be vapordeposited using chemical vapor deposition or physical vapor depositiontechniques. In certain embodiments, protective layer 1902 can be appliedas a low viscosity liquid to dendritic structure 1920 and the uppersurface of substrate 1914.

Typically, both vapor and liquid deposition techniques are performed ina reduced-pressure environment to ensure that protective layer 1902fills small gaps between the structural features of dendritic structure1920. In some embodiments, for example, vapor and/or liquid depositionof protective layer 1902 is performed at an ambient pressure of 100 Torror less (e.g., 50 Torr or less, 30 Torr or less, 20 Torr or less, 10Torr or less, 5 Torr or less, 1 Torr or less, 500 mTorr or less, 300mTorr or less, 100 mTorr or less).

Following deposition of protective layer 1902, in certain embodiments,the protective layer is hardened. Hardening of protective layer 1902 canbe performed by physical or chemical techniques. Suitable physicaltechniques for hardening protective layer 1902 include directing a flowof air onto protective layer 1902, heating the encapsulated dendritictag to cure protective layer 1902, and/or photocuring protective layer1902 by exposing protective layer 1902 to radiation, e.g., ultravioletradiation. Suitable chemical techniques for hardening protective layer1902 include, for example, exposing protective layer 1902 to chemicalcrosslinking agents such as formaldehyde.

In general, the material from which protective layer 1902 is formed ischosen for its particular physical and chemical properties to ensurethat the dendritic tag it encapsulates is protected from degradation ina variety of different environments. A variety of different materialscan be used singly, or in combination, to form protective layer. In someembodiments, protective layer 1902 includes cyanoacrylate, alow-viscosity liquid. A protective layer formed from cyanoacrylate canbe hardened by chemical reaction with water and/or by exposure toultraviolet radiation. Hardening yields a hard acrylic coating overdendritic structure 1920.

In certain embodiments, protective layer 1902 includespolymethylmethacrylate (PMMA), which can be deposited either as a vaporor a liquid onto the dendritic tag, and hardened by chemical reactionwith a peroxide material or exposure to ultraviolet radiation. Thehardened PMMA forms an acrylic layer that encapsulates dendriticstructure 1920.

In some embodiments, protective layer 1902 includes polysiloxane, whichcan be deposited either as a vapor or a liquid onto the dendritic tag.Hardening of polysiloxane by thermal curing yields a silicate coatingthat encapsulates dendritic structure 1920.

In certain embodiments, protective layer 1902 includes polyethylene,e.g., polyethylene terephthalate (PET), which can be deposited either asa vapor or liquid onto the dendritic tag (e.g., as a monomer) andhardened by chemical reaction or exposure to heat or ultravioletradiation. The hardened PET forms a layer than encapsulates dendriticstructure 1920.

In some embodiments, protective layer 1902 includes silicon dioxideand/or silicon nitride. These materials can be deposited by pyrolysis ofvapor sources in a chemical vapor deposition reaction, yielding a highlyconformal oxide and/or nitride film that encapsulates dendriticstructure 1920.

FIG. 20 shows a schematic diagram of another dendritic tag featuring asubstrate 2014 and a dendritic structure 2020 formed thereon. In FIG.20, the dendritic tag is not encapsulated by a protective layer 1902deposited from vapor or liquid to form a conformal film on the dendriticstructure. Instead, protective layer 2004 formed from a relatively soft,compliant material that is applied as a solid film over the dendritictag. The technique shown in FIG. 20 is particularly suitable forrelatively robust dendritic structures that resist deformation, as theapplication of protective layer 2004 exerts a downward force ondendritic structure 2020.

Dendritic structure 2020 is sandwiched between protective layer 2004 andsubstrate 2014 in FIG. 20, and may not be fully coated by protectivelayer 2004 (i.e., not all portions of dendritic structure 2020 may be incontact with protective layer 2004). Voids between protective layer 2004and dendritic structure 2020, such as voids 2006 and 2008, may trapgases or may enclose volumes in which the pressure is reduced relativeto ambient pressure. Following application of protective layer 2004 tothe dendritic tag, the protective layer can be hardened using any one ormore of the physical and chemical methods disclosed above.

A variety of materials can be used to form the solid protective layer2004 that is applied to the dendritic tag. Suitable materials include,but are not limited to, acrylic, polycarbonate, PMMA, PVC, and/or glass.

Following application of one or more protective layers, the encapsulateddendritic tag is protected from physical and chemical degradation by theenvironment, but is accessible for optical measurements and is alsoelectrically (e.g., capacitively) addressable. As such, the dendritictag can function as an identifier containing information that can be“read” by optical and electrical methods.

To duplicate the morphology of a specific dendritic structure on a tag,contact molding is the process most likely to be successful, as moldingcan replicate complex, minute structural features. To perform contactmolding of dendritic structures, which have three dimensional shapes,the protective layer(s) must be removed from the structures. Removalmight be attempted by either physical or chemical methods. However,because dendritic structures typically have Mohs hardness values of lessthan about 2.5, the encapsulated tags are likely to be damaged byphysical attempts to remove the one or more protective layers from thetags. As such, physical tampering with the structures is effectivelyprecluded by the fragility of the structures.

Chemical attempts to remove the one or more protective layers are alsolikely to result in damage to the dendritic structure, as the protectivelayers are considerably more chemically inert than the encapsulateddendritic structure, which has a high surface area. Accordingly,chemical methods for removing the protective layers are unlikely tosucceed without damaging the dendritic structures, and because bothchemical and physical methods for removal are likely to fail, tamperingwith the encapsulated dendritic structure—including contact molding ofthe structure—is effectively precluded.

Another technique that might be attempted to duplicate dendritic tagsinvolves optically scanning an intact tag and then duplicating the tagusing methods such as printing. However, these methods are effectivelyprecluded by the complex morphology of the dendritic structures in thetags. FIGS. 21A-C show a series of micrographs of dendritic structuresgrown on a substrate with an overlying liquid electrolyte. Themagnification increases from FIG. 21A through FIG. 21C. As is evidentfrom these figures, the morphology of the dendritic structures iscomplex and three dimensional, and extends to nanoscale dimensions.Morphologies of dendritic structures in the direction perpendicular tothe substrate surface typically differ, depending upon whether theelectrolyte used during fabrication was in solid form, or in liquid orgel form. Typically, liquid- or gel-based electrolytes yield dendriticstructures with significant growth along the perpendicular direction, asshown in FIGS. 21A-C. In contrast dendritic structures grown using asolid electrolyte typically have a “terrain-like” or “mountainous” shapein the perpendicular direction, as shown in the examples of FIGS. 22Aand 22B.

The three dimensional morphology of the dendritic structures makesreplication by top-down methods very difficult. Moreover, threedimensional printers do not have resolutions sufficient to replicatenano-scale features of dendritic structures. As such, the fractalcomplexity of the dendritic structures effectively preclude replicationof the structures using conventional methods. Further, application ofone or more protective layers using the methods disclosed herein canlead to minor, but unpredictable, distortions of dendritic structures.Even if methods were developed for the duplication of such structures,the duplicate structures would not necessarily undergo similardistortions when one or more protective layers are applied. This elementof unpredictability further ensures that duplication of the encapsulateddendritic tags is highly difficult.

The encapsulated dendritic tags disclosed herein can be used foridentification and authentication of articles such as commercial goods.In such applications, the tags are typically bonded to an outer surfaceof the articles. Removal of the tags from the articles to which they areaffixed for purposes of engaging in fraudulent activity is therefore animportant consideration. A variety of methods might be considered toeffect such removal, including mechanical (i.e., physical) methods wherea dendritic tag is carefully peeled, scraped, or cut from the article,thermal methods where heat is applied to the bond between the tag andthe article to weaken the bond and separate the tag from the article,and chemical methods in which a chemical agent such as a solvent or acidis used to soften or remove the bond between the tag and the article.However, each of these methods typically fails, as each method generallydestroys the dendritic structure underneath the one or more protectivelayers.

Destruction of a dendritic tag in the event an attempt is made to removethe tag from an article to which it is affixed provides a convenientmethod for ensuring that tags remain associated with the articles towhich they are applied, and are not applied to other articles. A varietyof additional steps can also be taken to ensure that attempts to removea tag from its associated article results in partial or completedestruction of the dendritic tag.

In some embodiments, to prevent removal of applied dendritic tags, astrong bonding agent is used to affix dendritic tags to specificarticles. The bonding agent can be, for example, a chemical adhesive, athermal bonding material, and/or an ultraviolet light-activated bondingagent.

The bonding agent used to affix dendritic tags to particular articlesunites the tags and articles via bonds that are stronger than the shearstrength of the tags. As a result, attempts to remove the tags from thearticles to which they are bonded typically result in tearing of thetags. In the encapsulated tags, the dendritic structures are typicallypositioned within 50 microns (e.g., within 40 microns, within 30microns, within 20 microns) of the adhesive layer to prevent sectioningof the tag between the adhesive layer and the dendritic structure, whichmight allow the dendritic structure to be removed from the article towhich it is affixed in intact form.

In some embodiments, a portion of the dendritic structure in a tag canbe bonded directly to an article to ensure that attempts to remove thetag from the article results in destruction of the tag's dendriticstructure. FIG. 23 is a schematic diagram showing a dendritic tag 2140bonded to an article 2112 using a layer of adhesive 2110. Dendritic tag2140 includes a substrate 2114 that supports a dendritic structure 2120,and a protective layer 2102.

As shown in FIG. 23, a portion of substrate 2114 has been removed, sothat a portion of dendritic structure 2120 is bonded directly to article2112 via adhesive 2110. As a result of the direct bond between dendriticstructure 2110 and article 2112, attempts to remove dendritic tag 2140from article 2112 are likely to result in damage to, or destruction of,dendritic structure 2120.

Although only a single portion of substrate 2114 has been removed toallowing bonding of dendritic structure 2120 to article 2112 in FIG. 23,more generally, one or more portions can be removed. The removedportions can be arranged in any desired pattern on substrate 2114.Suitable patterns can include two-dimensional array patterns (e.g.,criss-crossing patterns), for example. In certain embodiments, substrate2114 can be removed entirely and the entire dendritic structure 2120 canbe bonded to substrate 2114. Portions of the substrate may be removedusing techniques such as cutting, scribing, etching, and/or laserablation.

In certain embodiments, similar (or the same) materials are used to formboth protective layer 2102 and the adhesive layer that bonds dendritictag 2140 to article 2112. By using similar or the same materials, ifattempts are made to chemically dissolve or thermally soften theadhesive layer, damage will also occur to protective layer 2102, and todendritic structure 2120. In some embodiments, for example, protectivematerial 2102 and the adhesive layer are formed from a cyanoacrylateliquid, which is cured by a chemical reaction with water vapor in theenvironment. In certain embodiments, protective material 2102 and theadhesive layer are formed from a UV curable adhesive material.

In some embodiments, adhesive is applied in a patterned geometry betweendendritic tag 2140 and article 2112. The adhesive pattern can include,for example, a series of dots, stripes, or another regular or irregularpattern. By applying adhesive in a pattern, certain portions ofdendritic tag 2140 are bonded more firmly to article 2112 than otherportions. As a result, physical removal attempts are more likely tocause distortion or breakage of dendritic tag 2140.

In certain embodiments, substrate 1114 can be patterned or roughened.FIG. 24 is a schematic diagram of a dendritic tag 2140 bonded withadhesive 2110 to an article 2112. The surface of substrate 2114 that isbonded to article 2112 is patterned with a series of grooves that arenot completely filled by adhesive 2110. As a result, the groove portionsof substrate 2114 are not bound as firmly to article 2112 as the otherportions of substrate 2114. Due to this uneven adhesion, attempts tophysically remove tag 2140 from article 2112 are more likely to lead todistortion or breakage of tag 2140.

In general, a variety of different types of patterned substrates can beused in FIG. 24. For example, in some embodiments, the patternedsubstrate features a plurality of grooves and/or recessed circular orelliptical regions. The pattern features can generally be arrangedregularly on substrate 2114 or in a random pattern.

In some embodiments, dendritic tag 2140 includes one or more mechanicaldefects deliberately introduced into the tag during fabrication so thatif an attempt is made to remove the tag from the article to which it isattached, the tag will tear. The mechanical defects can include avariety of scores, cuts, and other structural defects. FIG. 25 is aschematic diagram of a dendritic tag 2140 that includes a plurality ofcuts 2142 introduced so that a force is applied to the tag (e.g., in aneffort to peel it away from an article to which it is attached), the tagruptures along one or more of the cuts.

In certain embodiments, dendritic tags can be positioned in recessesformed in articles to make removing the tags more difficult. FIG. 26 isa schematic diagram showing a dendritic tag 2140 positioned in a recess2160 of an article 2112. By positioning tag 2140 in recess 2160,application of prying tools to peel the tag from the substrate is mademore difficult. A variety of different recess cross-sectional shapes canbe used, including square, circular, rectangular, elliptical, andpolygonal. In some embodiments, recesses with overhanging edges can beused, as these can be particularly effective at preventing prying of thetag from the article.

In some embodiments, additional materials can be included within thestructure of dendritic tags to trigger destruction of the tags iftampering occurs. For example, FIG. 27 shows an embodiment of adendritic tag 2140 bonded to an article 2112. Encapsulated by protectivelayer 2102 are dendritic structure 2120 and reactive materials 2170.Reactive materials 2170 can include any one or more of a variety ofmaterials that react when exposed to the environment around tag 2140(e.g., to air or water vapor in the environment). If an attempt is madeto remove protective layer 2102 from tag 2140, reactive materials 2170are exposed and react, destroying dendritic structure 2120 (e.g., bydissolving, discoloring, distorting, or destroying the morphology ofdendritic structure 2120) so that it cannot be duplicated.

A variety of different reactive materials can be used as shown in FIG.27, including solids, liquids, and gases. Examples of reactive materialsthat can be used include, but are not limited to, mild acids, oxidizers,and/or sulfidizing agents.

The reactive materials can also be arranged in a variety of ways in tag2140. In some embodiments, for example, reactive materials 2160 arearranged in discrete regions, as shown in FIG. 27. In certainembodiments, reactive materials 2160 are dispersed within one or morecomponents of the tag, such as within protective layer 2102. Tags withreactive materials can be fabricated using a multi-step encapsulationprocess following formation of the dendritic structures. First, thedendritic structure is coated to protect it, then a fragile blister thatincludes the reactive material is applied, and the dendritic structureon its substrate and the blister are encapsulated together.Alternatively, in some embodiments, the substrate is formed so that thereactive material is contained in a pocket or blister underneath thelocations where dendritic structures are to be grown; once grown on topof the pockets or blisters, the dendritic structures and reactivematerials are encapsulated together to form the tag.

In some embodiments, a covert tagging procedure can be used to applydendritic structure tags within a material or underneath the surface ofa material so that the structure is not visible on the material surface.Instead, a portion or all of the dendritic structure can be hiddenwithin or behind the material.

As described previously, metallic dendritic structures can be grownwithin a porous substrate such as filter paper or microfiber cloth bysoaking the substrate material with a liquid electrolyte solution andthen contacting the material with at least one anode and at least onecathode. When an electrical potential is applied between the anode(s)and cathode(s), dendritic structure growth occurs.

FIG. 67 is an image showing an example of a copper dendritic structurethat has been grown using such methods. Portions 6702 of the structuregrown at the surface are distinctly visible, whereas sub-surfaceportions 6704 and deep sub-surface portions 6706 are less visible, sothat the fine detail of the dendritic structure is obscured even at highmagnification under an optical microscope.

In embodiments where the dendritic structure is grown or applied to arigid or semi-rigid substrate such as a plastic substrate (e.g., acredit or access card), a thin (e.g., less than 100 μm thick) dyedplastic layer can be applied over the dendritic structure and fixed inplace with adhesive. Such layers are commonly used during cardfabrication to add graphical elements and/or security features (e.g.,holographic features) to the surface of cards, and can also be used tohide the presence of dendritic structures. Suitable materials that canbe used for such layers include, for example, polyvinyl chloride acetate(PVCA).

Dendritic structures applied to such substrates can be scanned usinginfrared light. Because such light is not visible to the human eye, eventhe scanning process can be performed covertly in certain embodiments.In general, the dendritic structures can be imaged with light having acentral wavelength between about 750 nm and about 2000 nm. Light withinthis wavelength range will readily pass through one or more plasticoverlayers.

In some embodiments, the dendritic structures can alternatively oradditionally be scanned using capacitive scanning methods. Suitablecapacitive scanning methods have been described above.

Commercial Applications

The dendritic tags disclosed herein feature dendritic structures, no twoof which are precisely identical. Because each dendritic structure isunique, a tag containing the structure can be affixed to an article toact as a “fingerprint” that uniquely identifies the article. Moreover,because dendritic tags can be economically fabricated in large volumesand protected against degradation, duplication, and removal, they areparticularly well suited for use in commercial transactions, whereidentification and authentication of goods is of great importance tomany commercial entities.

FIG. 28 is a schematic diagram showing a flow chart 2200 that includes aseries of steps for identifying and authenticating goods using dendritictags. In a first step 2202, a dendritic tag (e.g., any of the dendritictags disclosed herein) is applied to an article to uniquely mark thearticle. Any of the methods disclosed herein can be used to apply thetag to the article, including, for example, bonding the tag to thearticle using a layer of adhesive material.

After the tag is applied to the article, the tag is scanned in step2204, and information about the tag that is obtained from the scan isstored, along with information about the article, in an electronicrecord. Methods for scanning a dendritic tag and for obtaininginformation about the tag from such scans are discussed in a subsequentsection. Typically, the information about the tag includes informationabout one or more morphological features of the tag that can be used torapidly identify the tag.

The electronic record that is created includes both the tag informationand information about the article, such as the type of article,information about one or more of its properties (e.g., size, shape,color, manufacturing origin, lot or identity number), and informationthat is used for inventory control (e.g., an inventory control number,warehouse location, inventory check-in and/or check-out dates).Typically, the electronic records are stored in a database (e.g., asecure database) that is accessible over a network. A variety ofdifferent networks can be used to access the database, including WiFinetworks, cellular data networks, wired networks, wide-area networks,and the internet.

Tracking of tagged articles can be performed for a variety of reasons.In some embodiments, for example, the tagged article is moving through aportion of a corporation's supply chain, e.g., from a storage facilityto a manufacturing site, from a factory to a storage warehouse, from afactory to a retail location, from a factory or warehouse to adistribution facility, from a first factory to a second factory, or evenbetween two locations at the same site, e.g., between two locations on amanufacturing or assembly line. In certain embodiments, the taggedarticle is being transferred from a seller of the article to a purchaserof the article. In some embodiments, the tagged article constitutes rawmaterial for a manufacturing process, and is being transferred to anentity that is contracted to refine the raw material.

In the foregoing and other scenarios, the tagged article, after beingscanned and the scan information stored, is transferred to the recipientof the article in step 2206. Then, in step 2208, the recipient scans thedendritic tag applied to the article in a manner similar to step 2204.The scan is analyzed to determine information about the tag, in a mannersimilar to the manner in which the tag information is determined in step2204.

Next, in step 2210, the previously scanned tag information is obtained.In some embodiments, such as when the tagged article is beingtransferred between two points in a single entity's supply chain, boththe sender and recipient of the tagged article will have access to thesame secure database where the tag information is stored, and so thepreviously scanned tag information can simply be retrieved from thedatabase. This scenario applies, for example, when the tagged article istransferred from an entity's manufacturing facility to a storage,distribution, or retail facility. When the tagged article is scannedupon receipt in step 2208, other information about the article, such asthe article's location, condition, inventory information, and/or price,can be entered into the database to update the article's electronicrecord.

If the tagged article is transferred to a retail facility, the owner ofthe article (e.g., the seller) may allow potential buyers of the articleto scan the tag applied to the article and to access the owner'sdatabase to obtain the previously-scanned information about the tag.This permits potential buyers to verify for themselves that the articleis genuine.

If the tagged article is being transferred from one entity to another,separate entity (e.g., in a commercial transaction between a seller anda buyer, such as a transaction that occurs over the internet), theinitial scan and determination of tag information would be performed bythe seller, and the subsequent scan and determination of tag informationwould be performed by the buyer. In this scenario, the seller would haveto be trusted to reliably provide the previously-determined taginformation at a later date.

A variety of different methods can be used to ensure that the sellerreliably provide this information. In some embodiments, for example,sellers can be certified by an independent monitoring authority andmonitored for compliance with a business code of conduct. Buyers wouldtherefore receive some assurance that sellers who receive thiscertification can be trusted to provide the previously scanned taginformation.

Suppliers can also be certified by an independent authority. Forexample, in transactions where a buyer purchases an article from a firstcommercial entity (i.e., the seller) and the article is shipped directlyto the buyer from a second commercial entity (i.e., the supplier), thesupplier performs the initial scan of the tag applied to the article instep 2204. The buyer, who receives the article from the supplier,performs the second scan of the tag in step 2208. As describedpreviously, the supplier is trusted to provide the previously scannedtag information on demand to verify the authenticity of the article.

Next, in step 2212, the previously scanned tag information (i.e., fromstep 2204, provided in step 2210) is compared to the scanned taginformation determined in step 2208 to identify the tagged article. Insome embodiments, the comparison can be performed by the recipient ofthe tagged article. For example, the same device used to scan the tagand determine the tag information in step 2208 can be used to comparethe tag information to previously-determined tag information to identifythe tagged article. The device can include an electronic processorexecuting software instructions that perform this comparison.

Alternatively, in some embodiments, the recipient of the tagged articlecan transfer the scanned tag information determined in step 2208 to adifferent device, such as a remote computer, that performs thecomparison. The information can be transferred over a network, e.g., anyof the previously described networks, or over a direct wired connectionto the computer. The remote computer includes an electronic processorexecuting software instructions that perform the comparison. In certainembodiments, the remote computer is owned by the recipient of the taggedarticle. In some embodiments, however, the remote computer is owned by aseparate entity, such as a transaction clearinghouse, that performs thecomparison and reports the results to the recipient (and, optionally, tothe seller or supplier of the tagged article).

In the event the identity of the article is confirmed by the comparisonin step 2212, the transaction between the sender and recipient of thetagged article is concluded. However, if the identity of the article isnot confirmed (e.g., the comparison of the previously determined taginformation and the newer tag information does not yield a match), thenthe recipient and sender of the tagged article can take further steps toresolve the discrepancy. The steps can include, for example, return ofthe tagged article to the sender. In either scenario, the process shownin flow chart 2200 terminates at step 2214.

At steps 2204 and 2208 in flow chart 2200, the dendritic tag applied tothe article is scanned to obtain tag information. The scanning step canbe performed in a variety of locations, including on a manufacturing orassembly line, in a packing facility, on a shipping and/or receivingdock, in a warehouse, in a retail location, and in a buyer's home. Assuch, a variety of different devices can be used to scan and determinetag information. For example, in some embodiments, a dedicated scanningdevice is used. The scanning device can be an automated device thatautomatically scans tagged articles as they move through a manufacturingor warehouse facility. Alternatively, the scanning device can be aportable, handheld device.

FIG. 29 is a schematic diagram of an embodiment of a scanning device2300 for scanning a tagged article and determining tag information. InFIG. 29, an article 2350 with a dendritic tag 2360 applied thereto ispositioned in proximity to scanning device 2300. Device 2300 includes anoptional radiation source 2302, optional illumination optics 2304,optional imaging optics 2306, a detector 2308, an electronic processor2310, and a receiver/transmitter 2314. These components are enclosedwithin housing 2316. Device 2300 can optionally include a display 2312.An activation switch 2318 is optionally mounted to housing 2316.Radiation source 2302, detector 2308, receiver/transmitter 2314, display2312, and switch 2318 are connected to electronic processor 2310. Notshown in FIG. 29 is a power source (e.g., an AC power connection, or aportable power source such as a battery) that provides electrical powerto the components of device 2300.

Scanning of tag 2360 is typically initiated when a user of device 2300activates switch 2318. In embodiments where device 2300 is an automatedscanner, initiation of a scan can occur, for example, when article 2350passes through a specific location on a manufacturing or assembly line,triggering an external switch connected to electronic processor 2310.

When a scan is initiated, electronic processor directs radiation source2302, if present in device 2300, to illuminate article 2350 (and tag2360) with light through aperture 2320. Light reflected from tag 2360(i.e., illumination light and/or ambient light) enters housing 2316through aperture 2322, and is collimated and imaged by imaging optics2306 onto an active surface of detector 2308. Detector 2308 captures animage of tag 2360 which is then transferred to electronic processor2310. Electronic processor 2310 can optionally analyze the tag image toextract tag information. The image and/or the extracted tag informationis transferred to a database by electronic processor 2310 usingtransmitter/receiver 2314.

When display 2312 is present in device 2300, electronic processor 2310can also display a variety of messages on display 2312 to advise theuser of device 2300 of the progress of the scanning operation. Messagescan advise the user, for example, that a scan has been initiated, thatthe tag image has been acquired, and that tag information extracted fromthe image is being transferred to a database. As will be explained ingreater detail subsequently, display 2312 can also be used to displaymessages alerting the user that previously scanned tag information isbeing obtained from a database, that the previously scanned taginformation is being compared to more recently scanned tag information,and the results of the comparison to determine authenticity of thetagged article.

Radiation source 2302 can typically include any one or more of a varietyof light sources such as, for example, incandescent, fluorescent,LED-based, and/or laser-based sources. Detector 2308 can include one ormore imaging detectors, such as detectors based on a charge-coupleddevice (CCD) and/or detectors based on a complementary metal-oxidesemiconductor (CMOS) array. Transmitter/receiver 2314 typically featurescomponents, including signal modulation and demodulation components,that permit communication of information, e.g., in packet form, over oneor more wired or wireless networks or interfaces including, for example,WiFi networks, Bluetooth® networks, local area networks, wide areanetworks, the internet, cellular data networks, and direct wiredconnections to other devices.

In some embodiments, dendritic tags applied to articles can be scannedusing mobile telephones. For example, an application running on a mobiletelephone's electronic processor can use the telephone's built-in camerato acquire an image of a tag attached to an article. The telephone'selectronic processor can optionally analyze the image to extract taginformation, and then transfer the tag information and/or the image to adatabase over a wireless cellular data network using the telephone'sbuilt-in transceiver.

Because dendritic structures have considerable structural detail andcomplexity that can be used as unique identifying information, thestandard camera in a mobile telephone may not be able to capture imageswith sufficient resolution to provide tag information of sufficientquality for purposes of authenticating tags. In certain embodiments, anenhanced imaging module can be used together with a mobile telephone toyield images with enhanced resolution.

FIG. 30 is a schematic diagram showing a detachable imaging module 2408connected to a mobile telephone 2402 for scanning tagged articles.Mobile telephone 2402 includes an image sensor 2406 and, optionally, aflash unit 2404. Module 2408 can connect to mobile telephone 2402 usinga variety of mechanisms. In some embodiments, for example, module 2408snaps onto the housing of mobile telephone 2402; the interference fitensures that module 2408 remains in position relative to telephone 2402while tagged articles are scanned. In certain embodiments, module 2408can be attached to the mobile telephone 2402 using clips, temporaryadhesives, and/or magnets.

Module 2408 includes a lens 2412 and, optionally, a waveguide 2410. Lens2412 is positioned within module 2408 so that when module 2408 isconnected to mobile telephone 2402, lens 2412 aligns with image sensor2406. In this manner, lens 2412 can provide enhanced imaging of objects(i.e., enhanced relative to images that would be obtained using only themobile telephone's image sensor 2406 and internal optics). Although lens2412 is depicted as a single optical element in FIG. 30, more generallylens 2412 can include one or more optical elements. For example, in someembodiments, lens 2412 can be a compound lens that includes two or moreoptical elements. Each of the one or more optical elements of lens 2412can be formed from a variety of materials including various amorphousoptical glasses (e.g., fused silica), various crystalline materials(e.g., quartz, calcium fluoride), and various plastic materials (e.g.,polycarbonates, acrylics).

Module 2408 also optionally includes a waveguide 2410. Waveguide 2410 ispositioned within module 2408 so that when module 2408 is connected tomobile telephone 2402, illumination light generated by the mobiletelephone's flash unit 2404 (if present) is coupled into waveguide 2412and directed to be incident on an object to be imaged. Waveguide 2410can be formed from a variety of optical materials including, forexample, any of the materials disclosed above in connection with lens2412.

Although the foregoing optical elements are part of module 2408 in FIG.30, in some embodiments, some or all of the optical elements can bebuilt into the mobile telephone housing. For example, lens 2412 and/orwaveguide 2410 can be integrated within the housing of mobile telephone2402.

In some embodiments, certain exterior surfaces of waveguide 2410 can becoated with reflective optical materials to enhance the confinement andguiding of light from flash unit 2404 within the waveguide. For example,in FIG. 30, a reflective coating 2414 is applied to a portion of thedownward-facing surface of waveguide 2410. The uncoated surfaces ofwaveguide 2410 can function as apertures through which light can becoupled into waveguide 2410 (e.g., light 2420 generated by flash unit2404) or coupled out of waveguide 2410 (e.g., light 2422 that isincident on dendritic tag 2416 applied to article 2418). In general, avariety of reflective materials can be used to coat surfaces ofwaveguide 2410. Suitable examples include, but are not limited to,metallic materials such as aluminum, silver, gold, and nickel, andreflective dielectric multilayer materials.

Although waveguide 2410 is rectangular in shape in FIG. 30, moregenerally, waveguide 2410 can have a variety of shapes. In someembodiments, for example, waveguide 2410 can be tapered laterally in thedirection toward lens 2412 (i.e., in the direction from left to right inFIG. 30). Tapering waveguide 2410 in this manner can produce brighterillumination over a smaller spatial region by confining the guided lightrays spatially. Enhanced illumination can be useful, for example, whenimaging tagged articles in environments where ambient light is low.

Scanning of dendritic tag 2416 is typically initiated by a user ofmobile telephone 2402. In some embodiments, the user can acquire one ormore images of dendritic tag 2416 using the mobile telephone's software.That is, by connecting module 2408 to mobile telephone 2402 and thenactivating the telephone's image capture software, images of sufficientquality for dendritic tag analysis can be obtained. Alternatively, insome embodiments, a specialized application can be provided on mobiletelephone 2402. By activating an on-screen control provided by theapplication, the user can initiate image capture by sensor 2406. Imagesof tag 2416 obtained using either of the foregoing methods can be storedin mobile telephone 2402 (i.e., in a memory unit of the telephone and/orin an on-board storage unit, such as a flash memory device) for furtherprocessing.

In some embodiments, imaging of dendritic tag 2416 can be facilitated byproviding an optical element such as a lens on the surface of tag 2416.FIG. 31A is a schematic diagram of an article 2418 that includes adendritic tag 2416. Dendritic tag 2416 includes a dendritic structure2430 enveloped in a protective layer 2432. To facilitate imaging ofdendritic structure 2430, a lens 2434 is formed in protective layer2432. Lens 2434 can include a variety of different types of lensesincluding, for example, curved lenses (i.e., concave and/or convexlenses) and Fresnel lenses.

In general, lens 2434 is integrally formed in protective layer 2432.Various techniques can be used to form lens 2434. In some embodiments,for example, lens 2434 can be molded into protective layer 2432 asprotective layer 2432 is applied over dendritic structure 2430. Lens2434 can be molded, for example, using a form, having the inverse shapeof the lens, which is pressed into the protective layer material priorto hardening so that the material takes on the shape of the lens. Incertain embodiments, lens 2434 can be formed in protective layer 2432after the protective layer has been applied over dendritic structure2430. Various methods can be used to form lens 2434 including, forexample, mechanical cutting and/or grinding of protective layer 2432,ion etching of protective layer 2432, liquid-phase etching of protectivelayer 2432, and/or laser ablation of protective layer 2432.Computer-based machining systems that include three-axis roboticpositioning systems can be used to accurately etch, cut, or grindprotective layer 2432 using the foregoing methods.

In some embodiments, to facilitate imaging of dendritic structures, alens can be applied to the protecting layer that encapsulates thedendritic structure in a dendritic tag. FIG. 31B is a schematic diagramshowing an article 2418 that includes a tag 2416. Dendritic tag 2416includes a dendritic structure 2416 and a protective layer 2432.Further, lens 2436 is applied to a surface of tag 2416. Lens 2436 caninclude a variety of different types of lenses including, for example,curved lenses (i.e., concave and/or convex lenses) and Fresnel lenses.Various methods can be used to attach lens 2436 to protective layer2432. In some embodiments, for example, lens 2436 is glued to protectivelayer 2432 using an adhesive material. The adhesive material can, forexample, be an optical adhesive.

In certain embodiments, dendritic structures can be “imaged”electronically. For example, a capacitive array detector with aprotective coating that functions as a dielectric layer between thearray detector and the dendritic structure can readily be used to mapthe surface relief of the dendritic structure. Using such methods,features that are “higher” (e.g., extend further in a directionperpendicular to the general plane of the dendritic structure) havehigher capacitance values, as they are closer to the capacitive array.Examples of methods for capacitive reading of dendritic structures aredescribed above.

In some embodiments, dendritic tags can be used to secure articlesagainst tampering. Tampering can include, for example, attempts ataltering the contents of a package, improperly modifying an article, andreverse-engineering an article. The dendritic tags disclosed herein canmake these actions difficult, prohibitively expensive, and difficult, sothat attempts to do so are effectively discouraged.

In anti-tampering applications, a dendritic tag is applied to secure anarticle and scanned into a secure database, as discussed above, so aone-to-one mapping exists in the database between the specific structureof the tag and the article. The tag is applied to the article in theform of a seal over an opening in the article's housing or packaging sothat unauthorized access to the interior of the article, e.g.,disassembly of the article, will damage the tag. When the tag isre-scanned for purposes of identification, the damage to the tag willhave altered its structure in a manner that prevents successfulidentification. Further, the complex, three-dimensional structure of thetag ensures that it cannot easily or economically be duplicated. Thus,tampering with the article cannot be masked by fraudulent copying of thedendritic tag seal. At the same time, authorized maintenance performedon the article can be accompanied by replacement of the tag with a newtag, which is scanned into the database and associated with the article,replacing the record of the old tag.

Dendritic tags can be placed in a variety of ways to enhanceanti-tampering protection, depending upon the nature of the article tobe secured. For example, for articles that include a casing or housing,tags can be positioned across a break or seam in the casing (eitherexternally or internally) so that opening of casing, e.g., by removingan access panel, will break, damage, or distort the tag. For fastenerssuch as screws, bolts, and rivets that are installed in an article, tagscan be positioned on the head of the fastener so that significant forcecannot be applied to the fastener without damaging the applied tags. Thetags can also be applied such that they bridge the fastener head to asurface, so that removal of the fastener would break the tag.

In some embodiments, where the article includes a socket (e.g., anelectrical and/or data socket such as a USB port), the tags can beapplied across the socket either internally or externally to secure thesocket. If a member, such as a connector, is inserted into the socket,the tag will be damaged. Similarly, a tag can be applied to bridge thesocket and an inserted connector so that if the connector is removed,the tag will be damaged. In certain embodiments, where the articleincludes a valve, a switch, or a similar control device, tags can beapplied to the control device so that if the setting of the device ischanged, the applied tag will be damaged.

As discussed above, in some embodiments, dendritic structures in tagscan be fabricated so that they are degraded by exposure to light, heat,or various chemical substances. These properties can be applied tosecure tagged articles against tampering. For example, silver dendriticstructures, when exposed to light, typically partially dissolve intoelectrolyte films, which results in significant distortion of thestructures. A dendritic tag with a silver dendritic structure cantherefore be applied to secure a critical component of an articleagainst tampering, e.g., by positioning the tag inside the criticalcomponent so that opening the component's housing would expose the tagto light. Scanning of the exposed tag would reveal the distorteddendritic pattern, indicating possible tampering with the component.

In certain embodiments, a dendritic tag applied to secure an article canbe chemically sensitized so that it reacts with substances that arecommonly used to etch through coatings or housings of the article. Ifthe region of the article where the tag is applied can be evacuated, thetag can be sensitized to react in air. Reaction of the tag in air or toetching substances will distort the tag's dendritic structure,indicating possible tampering with the article.

In some embodiments, a dendritic tag applied to secure an article can befabricated in a manner such that when heated, the tag distorts, causingdisruption to its dendritic structure. For example, the dendriticstructure can be supported by a material (e.g., a plastic material)which exhibits hysteresis upon heating, and does not return to itsoriginal size and shape. Distortion of the tag, such as when the articleis heated to cause damage or obtain access thereto, is indicated by thedisruption to the tag's dendritic structure.

In certain embodiments, the dendritic tags disclosed herein can be usedto track and secure a wide variety of foodstuffs, both manufactured andharvested. Spoilage and contamination of food, and food poisoning viaingestion of spoiled and/or contaminated food, are worldwide problemsthat can affect large numbers of people in relatively concentratedgeographic regions when delivery of such foodstuffs occurs. For purposesof tracking food inventory to its source, existing RFID tags arerelatively costly, which precludes tagging each food item. Instead,tagging generally occurs at the pallet or shipment level. As aconsequence, the granularity of tracking is relatively coarse;individually packed items typically cannot be tracked.

The cost of RFID tags and their accompanying tag-reading technology hasdelayed deployment for purposes of food tracking. At present, only a fewmajor producers or suppliers have incorporated the technology into theirsupply chains. This patchwork deployment allows spoiled and contaminatedfoodstuffs to be offered for sale, and makes tracking such itemsdifficult, since many will originate from suppliers who have notimplemented reliable tracking technologies.

In contrast, the dendritic tags disclosed herein can be used to trackand secure a wide variety of food items at low cost, using methods thatare easy, straightforward, and reliable to implement. Using the tagsdisclosed herein to track such items increases the speed and efficiencyof tracking, and also provides tracking results of significantly highergranularity than other methods, even allowing tracking of individuallypacked items and/or individual items within packages. As the tags arehighly economical to produce and unique, then can be attached toindividual food items, to subsets of items in a batch, and/or topackaging.

Using readily available devices (e.g., a smartphone-based scanner, or adedicated handheld scanner), food inspectors, suppliers, wholesalers,and even consumers can scan the tags applied to food items to obtaininformation about the items stored in database records. The informationcan include recall notices, information about the origin, date ofmanufacture, date of packaging, freshness, and even health-relatedinformation such as warnings about consuming the food items togetherwith incompatible items such as certain medications. A softwareapplication implemented on the smartphone or handheld scanner can belinked to the database to retrieve and display the information to theoperator of the smartphone or scanner.

In certain embodiments, “expiring” dendritic tags can be fabricated toprovide additional information to food handlers, sellers, and consumers.For example, through judicious choice of materials, dendritic tags thatare destroyed by similar biochemical environments that cause foodspoilage can be fabricated. Thus, when the food items to which the tagsare applied begin to spoil due to their biochemical environment, thesame environment causes the tags applied to such items to degrade sothat they can no longer be successfully scanned and used foridentification. A food seller, handler, or consumer scanning such a tagcan rapidly determine that the food associated with the tag has spoileddue to the apparent degradation of the tag.

As discussed above, certain fabrication methods can be used to preparedendritic tags that expire on their own. For example, tags that includea mild corrosive material can eventually expire as the corrosivematerial penetrates its blister pack and dissolves at least a portion ofthe dendritic structure in the tag. These dendritic tags expire on theirown after a certain time period, which can be selected duringfabrication by choosing the amount and concentration of the corrosivematerial and the nature of the blister pack or other material thatencapsulates the corrosive material. Such tags can be applied to fooditems to serve as a “freshness” indicator, with their expiration periodschosen to correspond to the expected period after which the tagged fooditems are no longer ideal for consumption.

In some embodiments, a dendritic tag can be applied to a food item bydirectly incorporating dendritic structures into the Price Look Up (PLU)sticker attached to the food item. FIG. 41 shows a PLU sticker 2600 witha dendritic structure 2610 applied. Methods for growing dendriticstructures directly on paper and other porous substrates, as disclosedpreviously, can be used to incorporate the dendritic structures into PLUstickers. PLU stickers are numbered, and assigned and administeredglobally by the International Federation for Produce Standards (IFPS),which maintains a database of PLU sticker information. Records in thePLU database can be augmented by, or linked to, additional informationrelating to specific food items that bear PLU labels with dendriticstructures applied. Thus, while originally intended to speed checkoutand provide better inventory control for supermarkets, PLU codes incombination with dendritic tags can also be used to provide enhancedtracking of individual food items and greater quality accountability atlow cost. Further, while PLU codes alone only cover classifications offood items (e.g., conventionally grown apples vs. organically grownapples), combining PLU labels with dendritic tags yields item-specificidentifiers that allow individual food items to be identified, checked,and traced back to their point of manufacture or harvesting.

In certain embodiments, dendritic tags can be applied directly to foodproduct labels. The dendritic structures can be fabricated directly onthe labels, using the label material (typically paper) as a substrate inthe fabrication process, as discussed above. Alternatively, dendritictags can be fabricated separately and then applied to food productlabels using the methods discussed above. FIG. 41 shows an example of afood label 2600 with a dendritic tag 2610 applied to the label.

By appropriate selection of materials, fabricated dendritic tags caneven be safe for consumption by humans and animals, so that dendritictags can be applied directly to food items (e.g., produce, includingfruits and vegetables, and various meat products) and consumed when thefood items are consumed. As an example, dendritic tags that includedendritic structures formed from silver are consumable; the amount ofsilver in such a structure is small and non-toxic, and may even havebeneficial anti-bacterial properties. Once applied to food products,dendritic tags can be scanned using the optical and/or electronicmethods described is other sections of this disclosure.

An important advantage of dendritic tags relative to other trackingtechnologies is radiation hardness. Cobalt-60 is frequently used forgamma-ray irradiation of a variety of food and other products forsterilization purposes, including red meat, poultry, spices, cosmeticingredients, and medical devices. Cobalt-60 sources typically producehigh energy gamma photons (e.g., 1.17 MeV and 1.33 MeV) that ionize theirradiated material, liberating electrons that disrupt the molecularstructures and DNA of living organisms such as bacteria, causing celldeath. Typical dose ranges for various sterilization applications are asfollows:

Disinfestation treatment of fruits and vegetables for 0.1-0.5 kGy exportPathogen reduction in meat and poultry 1-3 kGy Sanitation of spices 5-15kGy

Certain conventional electronic tracking technologies are moderately toseverely damaged by ionizing gamma ray radiation at the dose rangeslisted above. In particular, many RFID chips are damaged by suchradiation. Although certain RFID chips are available that arepurposefully fabricated to withstand such doses, these special chips aresignificantly more expensive than conventional chips. In contrast, thedendritic tags disclosed herein are essentially impervious to gamma rayirradiation, as they are not biological in nature and do not containelectronic circuit components. As a result, such tags are highlycompatible with food sterilization processes involving gamma rayirradiation, and can be applied directly to food items and/or packagingbefore irradiation without suffering degradation during sterilization.

In some embodiments, the dendritic tags disclosed herein are used tocounteract tampering and counterfeiting in the pharmaceutical industry,and the ensure quality control. While both of these problems aresignificant at present, counterfeiting is the most prevalent problem.Counterfeit and/or sub-standard medicines can have severe medicalrepercussions, including death, particularly since many medicines areadministered to vulnerable individuals who have existing healthproblems. Proposed technologies for tracking individual drugs andpackages in the pharmaceutical industry include edible microscopicsilica-based barcodes. However, such barcodes are challenging tomanufacture and handle, and require specialized scanning technology.

The dendritic tags disclosed herein can be applied to a wide variety ofpharmaceutical products and medical devices and used for identificationso that such products and devices can be tracked from their origin, andtampering and counterfeiting can be curtailed. In some embodiments, asshown in FIG. 42 for example, a label 2700 applied to a drug containercan include a dendritic tag 2710 that can be fabricated directly onlabel 2700, or fabricated separately and applied to label 2700. Suchtags can be applied to pharmacy-dispensed packaging, to originalpackaging at manufacture, to shipping containers, and to a variety oflabels applied to the products at intermediate points from the point ofmanufacture to the point of consumption.

In certain embodiments, consumable dendritic tags, disclosed above foruse with food items, can be applied to individual pills, capsules, andvials so that individual units of pharmaceutical products can beidentified.

As described above in connection with other applications, theapplication of dendritic tags to pharmaceutical products (e.g., drugs,cosmetics) and medical devices allows such products and devices to betracked throughout their product cycle by shippers, handlers, andconsumers to prevent tampering, counterfeiting, and the consumption oruse of expired or substandard pharmaceuticals and medical devices.Dendritic tags are applied to such products at the point of manufactureand their information entered into a secure database. Shippers,handlers, and consumers can scan the applied tags and connect to thedatabase to verify the identity of the tagged pharmaceuticals andmedical devices, and to retrieve other stored information about thetagged products.

When the dendritic tags are applied to medical devices such as syringes,pacemakers, stents, valves, and other implants, the hardness of thedendritic tags to Cobalt-60 gamma ray irradiation provides an importantadvantage, as discussed above. Gamma rays generated by Cobalt-60 sourcesare used to sterilize many different medical devices. Doses used tosterilize medical devices are typically much higher than those used tosterilize food items; some examples are shown below:

Sterilization of pharmaceuticals, cosmetics  5-15 kGy Sterilization ofmedical devices 25-35 kGy

Because they are non-biological and do not contain electroniccomponents, the dendritic tags disclosed herein remain largelyunaffected even by these higher radiation doses. As a result, they arewell suited for tracking articles such as medical devices that aresubject to sterilization procedures.

In addition to applying dendritic tags to a wide variety of products foridentification and tracking purposes, dendritic tags can also beintegrated into product container seals and/or closures to preventtampering with the product inside the container. By integrating the tagsinto the seals and/or closures, tampering with the product by opening orremoving the seals/closures damages the dendritic tags. The damage tothe tags is revealed when the tags are scanned, and the product can berejected as compromised.

One or more dendritic tags can be used for tamper prevention. FIG. 43 isa schematic cross-sectional diagram showing a product container 2800with a seal 2810 covering the opening into the container. Two dendritictags 2820 are positioned at the peripheral edges of seal 2810 where itis attached to the opening of container 2800. Opening container 2800 bymechanical removal of a portion of seal 2810 will lead to damaging oftags 2820, which damage is revealed when the tags are scanned. Moreover,because the dendritic structures in the tags have three-dimensionalstructure as discussed above, producing a duplicate tag by counterfeitmethods to mask the tampering would be very difficult.

In some embodiments, by judicious choice of materials, dendritic tagscan be fabricated that are degraded by one or more of exposure to heat,exposure to light, and exposure to certain chemical substances. As anexample, dendritic structures formed of silver can partially dissolveinto an electrolyte film when exposed to light, thereby significantlydistorting their structure. Such light-sensitive dendritic tags can beincorporated into packaging materials for products such that scanning ofthe tags, upon opening of the packaging materials under suitableconditions (e.g., in the absence of light), can reveal whether thepackaging has been opened prematurely, as premature opening will haveled to damage to the dendritic structure in the tags. Suchlight-sensitive tags can also be used as product quality indicators forproducts that cannot withstand prolonged exposure to light. Damage tolight-sensitive dendritic structures in the tags would suggest that thetagged products had been exposed to light at some point.

Heat-sensitive dendritic tags, which are fabricated from materials thatdeform when heated above a certain temperature threshold, can be used ina similar fashion. In particular, such tags can be applied to preventthe use of heating methods to tamper with product packaging, as theapplied heat will damage the dendritic structures in the tags. Further,for products that are heat-sensitive, the applied tags can reveal whenthe products have been exposed to potentially damaging temperatures,even if the exposure was accidental in nature and not due to tampering.

Dendritic tags that are degraded by exposure to certain chemicals canalso be used for both anti-tampering and product quality applications.In some embodiments, for example, dendritic tags that are chemicallysensitized to react with a variety of substances, including solventsused to dissolve product packaging adhesives, can be applied to packingmaterials. The use of such substances damages the dendritic structureswithin the tags, which is readily observed upon scanning the tags.Products with tags that are damaged can be flagged as potentially havingsuffered tampering. For even greater security in some applications,dendritic tags that are sensitive to one or more components of air canbe fabricated and applied to the interior of air-tight productcontainers, which can be evacuated or filled with inert gas prior toshipping. Opening such a container prematurely (i.e., tampering withsuch a container) will expose the tags to air, causing a chemicalreaction that damages the dendritic structures in the tags. Such damageis readily observed when the tags are scanned.

Moreover, for products that are air sensitive or sensitive to otherchemicals, dendritic tags with the same chemical sensitivity can beapplied, e.g., on the inside of product packaging. If damage to the tagsis revealed by scanning, the product can be flagged as possibly beingdamaged due to chemical exposure.

An important application for dendritic tags involves enhancing thesecurity of a variety of identification and security access cards,including driver's licenses, government and/or military identification,employee identification, student identification, building and/or roomaccess cards, computer access cards, passports, birth certificates,software access restrictions, and similar trusted identification andaccess cards, documents, and barriers.

Current security access technologies range from simple keys toelectronic key cards for physical access, and password schemes andfingerprint scanners for computer access. Conventional mechanical keysare easy to duplicate and are subject to loss and theft. Key cards,although they implement a variety of different technologies (e.g.,magnetic stripe encoding, RFID and/or NFC chips) can also be duplicatedor read using a variety of widely available technologies (e.g., magneticstripe data is easily scanned, and data from RFID and/or NFC chips canbe hijacked during transfer using appropriate scanners). Passwords usedto access physical locations and computer systems can be stolen viakeystroke logging software, and if too simple, can be discovered using avariety of brute force attacks. Moreover, passwords are easilydisseminated among multiple individuals, making access restrictions moredifficult to monitor and necessitating frequent password changes whichare inconvenient. Fingerprint scanners can be relatively simple todefeat and, as they implement optical scanning technology, may requiremore frequent maintenance and calibration as components of the systemage.

The dendritic tags disclosed herein provide an alternative or asupplement to the various technologies discussed above for enhancingsecurity in a wide variety of applications. Dendritic tags are easy toread and yet are difficult to duplicate due to their inherentcomplexity, which is due to natural stochastic electrochemical growthprocesses. Branching fractal dendritic structures are inherently complexfrom millimeter to sub-micron length scales and are alsothree-dimensional in nature. These complex shapes coupled with a toughprotective layer over the relatively fragile structures make themdifficult to dismantle and copy economically.

The dendritic structure in each tag defines a “code” through itsspecific physical structure that is unique to the tag. When stored inencrypted form in a database, the code can uniquely identify the articleto which the tag is attached, which allows access restrictions to beimplemented. Scanning the tags does not involve the generation ofdetectable RF signals, insulating the tags from electroniceavesdropping.

The tags are inexpensive to produce and can be applied at minimal costto a wide variety of articles. Dendritic tags can be very small (e.g., afew millimeters in diameter), and therefore consist of very littlematerial. Moreover, the tags can be mass produced using roll-to-rolltechniques at minimal unit cost. Although dedicated scanners can be usedto read the tags, they can also be readily scanned using conventionalsmartphones either in unmodified or modified form, making use of thesmartphone's inherent communication capabilities to securely accessremote databases. Tags that have been damaged or lost can have theirrecords easily purged from databases, making future attempts to use,duplicate, or transfer the tag all but impossible. Further, they can bereplaced by newer tags which can be scanned and readily entered intodatabases as replacements.

In addition to documents and identification/access cards, wristbands,and other similar key replacements, dendritic tags can be applied to awide variety of personal items such as watches, wallets, mobile phones,jewelry (e.g., rings, bracelets, pendants), credit cards, and businesscards. Due to their small size (e.g., a few millimeters in diameter),they are unobtrusive, and yet can be readily scanned. Moreover, coatingmaterials used to protect the dendritic structures in the tags renderthe tags mechanically robust and resistant to damage andenvironment-induced degradation. If damage to a tag does occur, it canbe replaced rapidly and at low cost with another tag.

As discussed above, dendritic tags can be fabricated on a wide varietyof substrates, including various paper and plastic substrates. Inparticular, dendritic structures adhere well to porous materials such aspaper, and can be directly applied to paper documents during printing ofthe documents. Thus, the methods disclosed herein can be used tofabricate dendritic structures directly on a wide variety of differenttypes of identification cards and documents. Alternatively, or inaddition, the fabrication methods disclosed herein for dendritic tagscan be used to prepare tags which can then be applied to cards anddocuments. Single or multiple dendritic structures can be applied, wheremultiple structures/tags can provide even greater security in certaincircumstances. Further, dendritic tags can be grown directly on, orapplied to, other items of identification such as wristbands, key fobs,and labels, and to personal items such as watches, wallets, and jewelry.

Cards and documents with dendritic tags are scanned when the bearerpasses through an entrance or checkpoint. In addition to the informationthat is typically read from such cards and documents (e.g., the bearer'sidentity, photograph, fingerprints, etc.), the cards and documents arescanned (e.g., using a scanner of the type disclosed herein, which canalso be mounted to a doorway frame or integrated into a tabletopscanning unit) and the identity of the cards and documents are checkedby verifying information derived from the images of the dendriticstructures against database records.

Dendritic tags used for such purposes significantly enhance the securityof cards and documents. Because the dendritic structures in the tags arethree-dimensional in nature, fabricating accurate copies of thestructures is very difficult. As a result, duplication and/orcounterfeiting of such cards and documents is much more difficult thanfor conventional cards and documents, which typically employanti-counterfeiting technologies such as holograms that arecomparatively much easier to fabricate fraudulently.

In addition to cards and documents that relate to the identity of thebearer, dendritic tags can also be used to secure a variety of otherdocuments against tampering and counterfeiting. For example, asdiscussed above, currency, bearer bonds, cheques, contracts, and othertypes of commerce-related documents and legal documents can be tagged,so that attempts to alter or copy such documents can be detected byscanning the applied tags.

Access schemes based on identification via dendritic tags can beimplemented in a variety of ways. In some embodiments, for example, auser (e.g., a person who has been granted access to a physical location,to a piece of equipment or software) can be issued multiple tags. Theissued tags are uncommitted, e.g., they have not been associated in anencrypted and secured database with the user.

To “activate” his access, the user affixes one or more of the tags to anaccess card or personal object. For example, if the user habituallywears a watch, a dendritic tag can be applied to a portion of the watchthat is easy to scan. As another example, the user can apply a dendritictag to a credit card or other card-based item of identification, or to adedicated access card, which can implement other security features aswell (e.g., photo identification, a password code). Multiple tags can beapplied, e.g., to provide access to different physical locations orsystems. Alternatively, single tags can be used as universal access keysto all locations and systems to which a user has been granted access.

After application, the tag (or multiple tags) is initially scanned andinformation associated with the tag is entered into a secure database.The information can include the date on which the tag was scanned, thelocation at which the tag was scanned, the article to which the tag wasapplied, a variety of information about the user (e.g., name,photographic identification, access restrictions and permissions). Theinformation can include an image of the tag. The information can alsoinclude one or more features derived from analysis of images of the tag,as will be discussed in greater detail subsequently. The analysis can beperformed by a device operated by the user and information about thefeatures entered into the database. Alternatively, the user can transmitone or more images of the tag to a remote computing device (e.g., thesame device that hosts the database), and the remote device can performthe analysis to obtain feature information, and enter the featureinformation into the database.

After the information about the tag is entered into the database and therecord associated with the tag is activated, the object to which the tagis attached can be used as an access device (e.g., a key) to gain accessto secured locations, secured equipment and/or software, to lock andunlock doors, to arm and disarm security systems, and for a variety ofother security-related applications. The tag can be scanned during suchapplications using a mobile telephone, for example, or using a dedicatedscanner, which can be housed in a physically secure location.Identification of the user bearing the article to which the tag isattached can be performed in one or more steps, for exampling by usingpasswords, PINs, pre-selected verification images, single-usetime-limited access codes generated securely and transmitted to theuser. In some embodiments, these additional identification steps can beperformed only once, e.g., upon initial activation of the dendritic tag.Alternatively, in certain embodiments, the steps can be performedperiodically, or even each time the tagged article is scanned. Ingeneral, the nature and extent of the additional security measuresimplemented can be selected upon consideration of factors such as thelevel of security desired and user convenience.

The dendritic tag (or tags) applied to the article is scanned whenaccess to a location or to a piece of equipment or software is required,or another security-related event occurs. Information derived from thescan (e.g., features derived from analysis of one or more images of thetag) is compared to secure database records to identify the bearer ofthe article with the tag. If a match is found and the bearer's securitypermissions are appropriate, access is granted (e.g., a “unlock” signalis sent to a door or to equipment, or software access is permitted).Dedicated scanners can communicate with remote secured databases viawired and/or wireless communication interfaces to transmit information,unlock codes, and other signals. When a mobile telephone is used to scanthe dendritic tag, communication between the phone and a remote device(e.g., a remote server that hosts the database) can occur using wirelessnetwork protocols (e.g., via WiFi networks) and/or using mobiletelephone networks. In some embodiments, a version of the secureddatabase can be hosted directly on the scanner or mobile telephone; thishosted version can be automatically updated by periodic synchronizationwith a remote computing device. Communication between the scanner ormobile telephone and the mechanism that secures the location orequipment (e.g., a lock) can occur via encrypted wireless connections onnetworks such as Bluetooth® and/or WiFi networks, for example.

In some embodiments, databases can also store a variety of settingsassociated with each dendritic tag. Because each tag record isassociated with a particular user, various user preferences can bestored within the tag's secured record. Such preferences can include,for example, temperature and/or lighting levels in rooms the user ispermitted to gain access, and various software settings within softwareprograms the user can operate. In certain embodiments, the databaserecords can also include tracking information such as the date, time,and location at which the tag is scanned and security access requested.This information can be used to provide detailed reports on the user'sattempts to gain access.

If a dendritic tag applied to an article is damaged, lost, or stolen, orif the tag is to be updated (e.g., to provide enhanced security or togrant the user a different set of security permissions), the recordassociated with the old tag can be purged from the database, a new tagcan be applied to the article (or to a different article), and the newtag can be scanned and its information entered into the database. Oncethe secure record associated with the tag is activated (e.g., followingthe steps described above), the newly tagged article can be used forsecure access in the same manner as before.

Dendritic Tag Authentication and Identification

Dendritic structures of various types can be used in tags foridentification and authentication of articles. For example, generaltypes of dendritic structures that can be used include: radial, in whichtrunks of the dendritic structure extend from a central growth point;parallel, in which multiple trunks extend approximately in parallel froma common plane or surface; and multiple, in which the dendriticstructure includes several radial and/or parallel structures. FIGS.32A-C show examples of radial, parallel, and multiple dendriticstructures, respectively.

Each of the structures shown in FIGS. 32A-C features multiple trunks,each of which in turn has its own pattern of branches that form a uniquefractal pattern in the plane of FIGS. 32A-C. In addition, each dendriticstructure is three-dimensional, with fractal structure in the dimensionperpendicular to the plane of FIGS. 32A-C. The fractal pattern in theplane of FIGS. 32A-C typically resembles classical dendrites with atree-like geometry. In the perpendicular dimension, the fractalstructure can be dendritic, or may more closely resemble a terrain-like(e.g., mountain-like) form. FIGS. 33A and 33B show scanning electronmicrographs of dendritic structures with tree-like and terrain-likefractal structure in the perpendicular direction, respectively.

In general, dendritic structures that are grown in a liquid electrolytesolution which overlies an electrode and supplies ions from above theelectrode will have a tree-like fractal structure in the perpendiculardirection, extending into the liquid electrolyte. In contrast, dendriticstructures that are grown on a solid electrolyte will have aterrain-like fractal structure in the perpendicular direction, as ionsare supplied from below the growing structure and build-up the structurefrom its base. The fractal nature of both tree-like and terrain-likegeometries ensures that the general shapes of both types of dendriticstructures does not vary with scale, so that the structures appearinvariant in both low and high magnification images.

The height of features extending in the perpendicular direction for bothtree-like and terrain-like dendritic structures is influenced by growthconditions such as the applied potential difference, the appliedcurrent, and the growth time. For terrain-like dendritic structures, theheight of features extending in the perpendicular direction can also beinfluenced via the selection of specific solid electrolyte compositions.For example, using a germanium-rich chalcogenide glass doped with silverfor the solid electrolyte yields dendritic structures with features thatextend further in the perpendicular direction than using achalcogen-rich material for the solid electrolyte.

FIGS. 34A and 34B show electron micrographs of dendritic structuresgrown on different solid electrolytes. The dendritic structure of FIG.34A was grown on a chalcogen-rich solid electrolyte. The maximum heightof features extending in the perpendicular direction in FIG. 34A isapproximately 20 nm. The dendritic structure of FIG. 34B was grown on agermanium-rich solid electrolyte, and the maximum height of featuresextending in the perpendicular direction is approximately 100 nm.Increased growth in the perpendicular direction is commonly observed insolid electrolytes in which the metal-rich phases are distinct andseparate in the solid electrolyte. This tends to occur in chalcogen-poormaterials, e.g., Ge_(x)Se_(1-x), where x<0.33 (e.g., 0.33<x<0.5).

After a dendritic tag that includes at least one dendritic structure hasbeen applied to an article, the dendritic tag can subsequently be usedto identify the article. Identification can be desirable, for example,after the article has exchanged hands, been stored in a storagefacility, or otherwise remained un-inspected for a period of time.

FIG. 35 is a flow chart 2500 showing a series of steps for identifyingan article tagged with a dendritic tag. In the first step 2502, one ormore images of the dendritic tag are acquired. The images can beacquired using a variety of image capturing devices including, forexample, a dedicated scanning device as shown in FIG. 29, and/or amobile telephone with or without an imaging module, as shown in FIG. 30.

Next, in step 2504, the dendritic tag is authenticated. In the contextof this disclosure, authentication refers to the process of verifyingthat the dendritic tag is an actual dendritic tag and not a copy orreplica of a tag. As discussed above, dendritic structures havethree-dimensional fractal structure. In contrast, many two-dimensionalcopies or replicas have only two-dimensional structure. This differencein dimensionality can be used to authenticate tags featuring dendriticstructures.

In particular, to verify that a structure is indeed a dendriticstructure, multiple images of the structure can be obtained using lowangle illumination from different angles. A dendritic structure—whichincludes features that extend in the perpendicular direction—reflectslight from its different facets in the perpendicular direction.Accordingly, “bright” regions in the multiple images will change as afunction of the angle of illumination.

This technique is demonstrated in FIG. 36, which shows an image of aUnited States quarter illuminated with ambient fluorescent light and theflash unit of a mobile telephone. The telephone's image sensor was usedto obtain the image in FIG. 36 by imaging with a lens of module 2408attached to the telephone. The image shows a portion of the relief ofGeorge Washington on the surface of the quarter. The mobile telephone'sflash unit was positioned to the left of the relief in FIG. 36; as aresult, the left-facing relief elements are highlighted by theillumination.

Using similar illumination and image capture techniques for dendritictags, images of the dendritic structures therein can be obtained frommultiple illumination angles. In some embodiments, color filters can beused to filter the illumination light so that the illumination light isdistinguishable from ambient light in images of the dendritic tags. Byfiltering the illumination light (e.g., light generated from anillumination source such as a flash unit of a mobile telephone), onlythe edges of the dendritic structure that face the illumination sourceare illuminated with the filtered light, and therefore appear in adifferent color than other features in the image. In addition to, or asan alternative to, obtaining multiple images from different illuminationdirections, the device used to image the dendritic tag can also recordvideo of the dendritic tag illuminated from different directions,showing a varying pattern of illumination as the illumination directionchanges.

Analysis of the images can be performed to determine whether differentfeatures of the structures are highlighted as the illumination directionvaries by determining which regions appear brightest in each of theimages. In some embodiments, for example, as the reflected light changeswith illumination angle, a three-dimensional representation of the outerfacets of the dendritic feature can be constructed to convert intensityand position of the reflected light to the angle, height, and positionof the reflecting surfaces to verify that the features of the dendriticstructure are indeed three-dimensional in nature, and nottwo-dimensional. If the angles and heights of the reflecting surfacesall lie within a thin planar region, the likelihood that the structureis a copy rather than a true dendritic structure is increased. Thedistribution of angles and/or heights can be compared to a thresholdvalue or distribution to determine whether a particular dendriticstructure contained in the tag is authentic or not.

Alternatively, in some embodiments, the observed changes in reflectedlight angles and positions as a function of illumination direction aresufficient to establish that a dendritic structure is three-dimensional.The distribution of reflected light angles and/or positions can becompared to a threshold value or distribution for purposes ofestablishing an authentication of the dendritic structure contained inthe tag.

In either of the methods disclosed above, image processing is typicallybe performed in the device that captures the images. In someembodiments, however, some or all of the image processing functions canbe performed by a remote computing device (e.g., a remote server) bytransmitting some or all of the acquired images at various illuminationdirections and/or angles to the remote device. Alternatively, or inaddition, video of the changing light reflection as a function ofillumination angle and/or direction can be transmitted to the remotecomputing device and used to authenticate or reject the dendritic tag.

FIG. 44A shows an image of a dendritic structure formed of silver thatwas grown on a paper substrate. Although the dendritic structure in FIG.44A appears to be flat in a two-dimensional image, the dendriticstructure is actually three-dimensional. As described above, thethree-dimensional features of the dendritic structure can be used toauthenticate the structure as a real dendritic structure, and not atwo-dimensional copy of such a structure. FIG. 44B shows an image of thedendritic structure of FIG. 44A under perpendicular illumination (i.e.,normal to the paper surface) in an optical microscope. An enlarged imageof a portion of the structure is shown in FIG. 44C.

FIGS. 45A-D are images showing reflected light from the dendriticstructure shown in FIG. 44B, illuminated with white light from a LEDsource from the top, left side, right side, and bottom, respectively,relative to the orientation shown in FIG. 44B. In each of FIGS. 45A-D,the circled region corresponds to the growth origin of the dendriticstructure, and the rectangles enclose the high points of the dendriticstructure, measured in a direction normal to the paper surface.

The images in FIGS. 45A-D were processed using contrast filters and bydecreasing the overall brightness to yield the corresponding imagesshown in FIGS. 46A-D, which each include a series of small reflectedlight points or regions. The reflected light patterns shown in FIGS.46A-D effectively include reflected light from only the highest pointsin the dendritic structure. Comparing the images, it is evident thatdifferent patterns of reflected light are observed, depending upon theillumination direction. These differing patterns of reflected light fromdifferent illumination directions are characteristic of athree-dimensional dendritic structure, and confirm that what is beingimaged is a true dendritic structure and not a two-dimensional copy.

The differing patterns of reflected light for specific dendriticstructures are shown further in the images shown in FIGS. 47A-D. Thedendritic structure in FIGS. 47A and 47C was illuminated with whitelight from the top direction and from the left hand direction,respectively. and the reflected light images in FIGS. 47B and 47D wereobtained, respectively. Each of the images in FIGS. 47B and 47D wereadjusted in contrast and brightness to remove contributionscorresponding to scattering from the substrate. The reflected lightpatterns in FIGS. 47B and 47D differ significantly, which ischaracteristic of a three-dimensional dendritic structure.

In certain embodiments, reflected light images obtained by illuminatingthe dendritic structures with different colors of light can provideadditional information that can be used to authenticate the structures.For example, when the device used to illuminate the structures includesa tunable laser-based source, reflected light images corresponding toboth different illumination directions and different illuminationwavelengths can be obtained. Even when illumination occurs from a commondirection, when the illumination light is of a different wavelength,reflected light images of certain dendritic structures may appeardifferent, and these differences indicate that what is being imaged is atrue three-dimensional dendritic structure, not a two-dimensional copy.

In some embodiments, the three-dimensional nature of the dendriticstructure can be further confirmed by comparing the differing patternsof reflected light to database records that include patterns ofreflected light, as a function of illumination direction, for authenticdendritic tags. For example, the measured reflected light patterns canbe decomposed to identify “sources” of reflected light in each image,each source having a position, a size, and an integrated intensity. Someor all of these attributes of the identified sources can then becompared to similar information derived from database records todetermine whether the observed reflected light images match a particulardatabase record, thereby authenticating the tag from which the imageswere measured. As described above, the database records can also includepatterns of reflected light that correspond to illumination withdifferent wavelengths of light, and this information can also be usedtogether with, or as an alternative to, information derived from imagescorresponding to different illumination directions to authenticatespecific dendritic structures.

Using the foregoing methods, a dendritic tag applied to an article canbe either authenticated as genuine, or rejected as a likely counterfeitcopy or replica. Returning to FIG. 35, if the dendritic tag attached tothe article is authenticated, then in step 2506, the image(s) of thedendritic tag are analyzed to extract features of the dendriticstructure in the tag. In general, each of the analysis steps disclosedherein can be performed by the device used to acquire the tag image(s),or by a remote computing device (e.g., a server), after the image(s)has/have been transmitted to the remote device from the image capturedevice.

As a first step in the analysis, a captured image is typically adjustedto filter extraneous features and produce a line segment representationof the dendritic structure. The adjustment can take a variety of forms.In some embodiments, the image is adjusted by altering the contrastand/or brightness of a grayscale version of the image so that a thinnedrepresentation of the dendritic structure is produced. One or morereference patterns printed on the dendritic tag can be used for thispurpose. For example, the contrast and/or brightness of the image can bealtered so that two adjacent reference patterns on the tag have aparticular separation between them. The contrast and/or brightness ofall images of the same dendritic tag can then be adjusted so that ineach image, the separation between the two reference patterns is thesame. Alternatively, or in addition, in some embodiments edge detectionalgorithms can be used on a captured image to highlight the edges of thedendritic patterns and the thinned (line) version of the image isproduced by positioning lines of a single thickness at the meanpositions between paired edges. Lines may also be positioned at the meanpositions between paired edges, where the thickness of the lines dependson the spacing between the edges. During the production of thinned orline segment images from the original acquired images, curved segmentscan be replaced with sequences of straight lines to facilitate fasterimage analysis and digitized image comparison.

Line segments in the thinned image are not necessarily straight, butwill typically begin and end on minutiae, which are branching points orterminations that appear in the pattern defined by the dendriticstructure. A variety of different dendritic pattern coding schemes forthe analysis of the images can be used; a coding scheme is used toidentify minutiae by position and type in an image of the dendriticstructure. An example of a coding scheme for minutiae types is shown inTable 1.

TABLE 1 Designation Type Description C Center or Origin Center or Originof dendritic structure and origin of all trunks (position of growthcathode) N N-branch N^(th) branching point, bifurcation, or angular bendafter start point in a trunk T Termination End point of anynon-continuing line segment I Isolation Isolated point or start (i.e.,closest to Center or Origin) of isolated line segment or branch Z High ZElement that appears brighter due to larger height in perpendiculardirection than average

In addition to the minutiae types above, fiducials can be printed on adendritic tag. Fiducials can be used for a number of importantfunctions. In some embodiments, fiducials can be used to indicatedirections from which tags can be illuminated to obtained reflectedlight images of the dendritic structure(s) therein, as described above,to authenticate the tags. The fiducials provide indicators for users whoscan the tags as part of a supply chain, for example, to ensure that theimages that are obtained correspond to images that were used to generatedatabase information that was stored for the tags, and that is usedlater to authenticate and/or identify the tags.

In certain embodiments, fiducials are used as points of reference forthe analysis of the dendritic pattern. As an example, for radial tagswith a central growth point, the Center minutiae point can be thefiducial. Further, S vectors associated with the line segments of thedendritic pattern can be obtained through analysis. An S vectorcorresponds to a number set that defines the length and angle of a linesegment that extends between two minutiae points (M points).

FIGS. 37A-37C show steps in the analysis of an image of a portion of adendritic structure. In FIG. 37A, the contrast of the image has beenadjusted to thin the image, reducing the representation of the dendriticstructure to an apparent line pattern. In FIG. 37B, a partial analysisof the thinned image has been performed to identify minutiae points andline segments according to the coding scheme disclosed above. Linesegments are overlaid on the image. Identified minutiae points areoverlaid on the image as follows: Centers or Origins, open triangles; Nbranches, solid circles; Terminations, crossed circles; Isolations, opencircles; and High Z points, dotted circles.

FIG. 37C shows the complete pattern of M points and line segments (Svectors) after analysis of the dendritic structure from FIG. 37A iscomplete. As shown in this figure, the dendritic structure has beenreduced to a collection of features through the analysis, and furtheroperations—such as identification of the dendritic structure—can bebased on the set of identified features, rather than on the full imageof the dendritic structure.

A variety of different analysis techniques can be used to perform thefeature recognition shown in FIG. 37C. In some embodiments, for example,the scale-invariant feature transformation (SIFT) can be used. Thistechnique transforms an image into a collection of vectors, each ofwhich is invariant to translation, scaling, and rotation, and to acertain extent illumination changes and localized distortion.Scale-invariant feature transformations are disclosed, for example, inLowe, David G., “Object recognition from local scale-invariantfeatures,” Proceedings of the International Conference on ComputerVision 2, pp. 1150-1157 (1999), the entire contents of which areincorporated herein by reference.

SIFT methods are similar to object recognition mechanisms of the primatebrain as described, for example, in T. Serre et al., “A Theory of ObjectRecognition: Computations and Circuits in the Feedforward Path of theVentral Stream in Primate Visual Cortex,” Computer Science andArtificial Intelligence Laboratory Technical Report,MIT-CSAIL-TR-2005-082, Dec. 19, 2005, the entire contents of which areincorporated herein by reference. Image recognition algorithms of thistype can be applied to raw images (e.g., without adjustment to thin theimages) and are typically robust, particularly when training images areused. As such, these methods are well suited for identification offeatures in images of dendritic structures, which can be distorted byphysical damage to the tag that includes the structure, and/or byimperfect imaging conditions.

FIG. 38A shows an image of a dendritic structure that is used to train aSIFT algorithm for dendritic structure feature recognition. Key trainingfeatures in FIG. 38A have been identified to the algorithm by taggingwith crosses. In FIG. 38B, the trained SIFT algorithm operates on a newversion of the training image to identify features in the imagecorresponding to various types of M points. Specifically, in FIG. 38B,108 points corresponding to features of the dendritic structure wereautomatically identified.

Returning to FIG. 35, after the set of features corresponding to thedendritic tag has been identified in step 2506, the set of features iscompared to records in a database in step 2508 to identify the tag (andthe article to which the tag is attached). Typically, this step isperformed by a remote computing device to which the dendritic image(s)or extracted set of features have been transmitted. The remote computingdevice may also host the database, or be configured to access thedatabase over a secured connection.

If the set of features obtained through analysis in step 2506 issufficiently accurate, than a unique match to only one database recordwill occur, uniquely identifying the tag. As discussed above, thedatabase records are typically generated when dendritic tags are appliedto articles and scanned, prior to manufacture, shipment, or storage ofthe tagged articles. Database records are maintained in secure storageto prevent unauthorized access and alteration, and therefore function asan analogue of a fingerprint database for tagged articles.

In general, comparison between the set of features obtained by analysisof images of a particular dendritic tag and database records will yielda number of potential matches. Various methods can be used to determinewhich of these potential matches is correct, and whether the match issufficiently precise to properly identify the tag and the article towhich it is attached. In the following paragraphs, one example of amethod for comparing the set of features obtained from the dendriticimages to database records is disclosed, although it should beappreciated that other methods can also be used.

In some embodiments, a hierarchical comparison can be performed betweenthe set of features obtained by image analysis for a dendritic tag anddatabase records to identify the tag. For example, the comparison beginsfrom the center or origin of the dendritic pattern, and then extends insuccessive steps outward from the center or origin, i.e., from highdimensional features such as trunks and major branches to lowdimensional features such as minor branches and twigs. For eachsuccessive feature, only database records that also contain such afeature (as well as all of the other higher-dimensional featuresidentified for the tag) are further considered as possible matches. Thatis, at the beginning of the comparison, all of the database records areconsidered to be possible matches to the dendritic tag. As eachsuccessive feature of the tag is analyzed, the possible list of matchingdatabase records can be reduced by eliminating records that do notinclude the collective list of features analyzed to that point. Thus,analyses of each successive feature typically reduces the number ofrecords that can correspond to a possible match (so that each successiveanalysis reduces the number of database records that are examined).

For example, a radial dendritic structure may have several trunksoriginating from the center. The angles between these trunks can bedetermined and used as the first several “levels” in the hierarchicalcomparison tree (i.e., only stored records which include this set ofangles would be retained for consideration at subsequent levels in thecomparison tree). The next several levels in the tree can be based onfeatures such as the distance from the center of each trunk to the firstmajor branch. Subsequent levels can be based on features such as theangles of these branches to their respective trunks. The foregoingprovides examples of features which can be used to implement differentlevels of the comparison tree, but more generally, any of the featuresextracted from the captured images can be used, in any order.

In some embodiments, “box counting” methods can be used to generate aunique identifier for a dendritic structure that can then be compared toinformation in stored records for purposes of identification. Boxcounting methods are typically used to determine the fractal dimensionof a dendritic structure, and are hierarchical in nature. In thisapproach, an image of the dendritic structure is divided into squareboxes arranged in a grid pattern. The grid pattern can be aligned tofiducial marks applied to the tag that contains the structure.

Each box is then examined to determine whether or not it contains aportion of the dendritic structure. The output for this examination stepis binary: each box is assigned a value of zero if the box includes noportion of the dendritic structure, and a value of 1 if the box includesa portion of the structure. Typically, in an initial scan, a fine-scalegrid is used to digitize the image. Then, in subsequent pattern matchingoperations, a coarse-scale grid is used initially, and then the analysisis repeated with progressively finer-scale grids, e.g., halving thelength of the box for each analysis step, to produce a unique data setto represent the dendritic structure.

The analysis corresponding to the coarsest-scale is used to reject allthe stored patterns that do not match. Subsequent finer-scale grids areused to do the same, rejecting all non-matching patterns to reduce thetime it takes to complete the matching process. Thus, box countingmethods implement a hierarchical analysis, just as the feature-basedmethods discussed above.

The rate at which comparisons to stored patterns can be performed can besignificantly increased in some embodiments by eliminating regions thatcorrespond to no dendritic structure from further consideration asfiner-scale grids are used. The selective elimination of such regionsfrom further consideration is based upon the observation that if aparticular region contains no dendritic structure at a coarse scale,then that region (and portions thereof) will also contain no dendriticstructure at finer scales. Accordingly, such regions can be eliminatedfrom further consideration at successively finer scales, which cansignificantly reduce analysis time at later levels of the hierarchicalanalysis scheme.

The comparison between identified features of the tag and databaserecords, or the binary box counting analysis and database records,proceeds until all the non-conforming records are rejected and only onepossible match remains. Since the dendritic structures are fractal innature, this process is primarily limited by the magnification of theimage acquisition optics; the higher the magnification used, the greaterthe number of features (and therefore, levels in the hierarchicalcomparison tree) as smaller and smaller features toward the ends of eachbranch can be included in the analysis. In general, the informationdensity from the analysis increases according to the fractal dimensionof the dendritic structure.

If the comparison results in no matches between the feature setcorresponding to the tag and the database records, in certainembodiments the comparison between the feature set and the databaserecords can be repeated, with relaxed measurement tolerances to obtain amatch. In some embodiments, the device used to perform the comparisoncan prompt the user to re-scan the dendritic tag to obtain a new set ofimages, which can then be used to repeat the feature set analysis andcomparison to database records. The new set of images can also be usedto reduce measurement and/or acquisition errors in the original set oftag images, e.g., by combining the images to reduce noise and/oraberrations. As an example, the dendritic nature of the patterns allowsdefects in the acquired images to be rejected, as the line segmentsshould be continuous and branching so that gaps and isolated truncatedpoints can be ignored during the feature set analysis and subsequentcomparison to database records. Captured image blurring can becompensated by the thinning process described above (e.g., by replacingthe acquired image with line segments). Scale or magnificationdistortions can be overcome using Scale Invariant Feature Transformmethods, as described above.

If the comparison is repeated and no matches are once again foundbetween the feature set corresponding to the tag and the databaserecords, the device can issue a warning (e.g., a visual and/or auditorymessage or alert) that the tag could not be properly identified, and maynot be genuine.

If the comparison produces more than one possible match between thetag's feature set and the database records, then in some embodiments,the comparison can be repeated with tighter measurement tolerances toproduce a more accurate match. In certain embodiments, the device usedto perform the comparison can prompt the user to re-scan the dendritictag to obtain a new set of images, which can then be used to repeat thefeature set analysis and comparison to database records. The new imagescan also be combined with the previous images to reduce measurementand/or acquisition errors; the combined image information can then beused for the second comparison.

If multiple potential matches remain following the second comparison(and, possibly, additional subsequent comparisons), further informationcan be used to distinguish among the potential matches. In someembodiments, for example, contextual information can be used. Dendritictags can be applied to a wide variety of different articles, anddatabase records can include information relating not only to thefeatures of the dendritic structures in the tags, but also to thearticles to which the tags are applied. This contextual information canbe used to distinguish among potential matches.

For example, suppose that two database records correspond to potentialmatches for a dendritic tag, but the first record includes informationindicating that it corresponds to a tag applied to one type of articlesuch as a pharmaceutical product, while the second record includesinformation indicating that it corresponds to a tag applied to adifferent type of article such as a meat product. If the tag that isbeing identified is attached to a pharmaceutical product, thiscontextual information can be used to readily identify the first recordas a match, and to reject the second record.

In addition, information obtained from reflected light images can alsobe used to distinguish among multiple possible database records. Asdescribed above, reflected light images that correspond to differentillumination directions and/or different illumination wavelengthsproduce distinctive reflected light patterns from dendritic structures.Information derived from images of these patterns (and/or the imagesthemselves) can be stored in database records and used to distinguishamong records having feature sets that nominally each correspond to thefeature set of a dendritic tag that is subject to identification.

In the foregoing discussion, contextual and reflected light informationare used to distinguish among possible database record matches after thehierarchical comparison has been performed. More generally, however,this additional information can be incorporated at any level into thehierarchical comparison to filter out possible matches from among thedatabase records. For example, in some embodiments, this additionalinformation can be used at the first level, or at one of the first fivelevels, of the hierarchical comparison. In certain embodiments, usingcontextual and/or reflected light information early in the hierarchicalcomparison can significantly reduce the number of database records thatare considered at subsequent levels.

Following the comparison in step 2508, the tag is either identified asgenuine, or identification is deemed impossible, and the procedure endsat step 2510. In either case, a message can be delivered to the user ofthe imaging device (e.g., the dedicated scanner shown in FIG. 29 or amobile telephone) via a display screen. The user may be given the optionof re-scanning the dendritic tag to attempt identification again.

In some embodiments, the set of features associated with analyzedimage(s) of the dendritic tag can be stored in the database and markedas a record corresponding to an unknown and/or potential counterfeitarticle. Various criteria can be used for determining whether marking ofthe set of features should occur in the database. For example, thefailure to produce any matches in the early levels of the hierarchicalcomparison is much less likely to be due to measurement/digitizationerrors and so is more likely to indicate a counterfeit tag, whereas sucha failure in the advanced levels of the comparison could be due tomeasurement errors. Thus, records can be marked according to the firstlevel at which no match between the tag's feature set and the databaserecords occurs, with a threshold level value (e.g., 2 or 3) to establishwhether the record is marked as a likely counterfeit. Records can bemarked with a variety of information, including the date and/or locationof the most recent comparison to other database records, the first levelat which no match occurred between the tag's feature set and the otherrecords, and the likely or suspected reason for the failure to match anyrecords. By marking the record corresponding to the extracted featureset as corresponding to an unknown and/or potential counterfeit article,subsequent scans of the same tag can rapidly alert the user of thescanning device that the tagged article is suspect.

To enhance tracking of potential counterfeit tagged articles, in someembodiments, database records associated with tagged articles caninclude information about the number of times a tagged article has beensuccessfully identified. For example, for tags that are applied toarticles that are expected to be identified only once (i.e., uponreceipt of a shipment), multiple identification of the tags may indicateimproper, and even fraudulent, re-use of the tags. Accordingly, databaserecords can include information about the number of times a tag has beensuccessfully identified to assist in tracking such potential improperre-use. In some embodiments, database records can even be expungedfollowing the first (or more generally, the n^(th)) successfulidentification, particularly where the records are associated witharticles that are expected to identified only once (or more generally,only n times). Expunging such records can prevent improper re-use of thetags, as once the records are expunged, it would no longer be possibleto identify the tagged articles.

In certain embodiments, database records can also include otherinformation to assist in the identification and tracking of taggedarticles. For example, the records can include location informationabout where identification of specific tags occurred and/or wasattempted. This information can be transmitted from the device used toscan the tags (e.g., a dedicated device with a GPS transceiver, or amobile telephone with an on-board GPS chip). Analysis of the locationinformation can reveal information such as locations where attempts tofraudulently re-use or tamper with tags are particularly prevalent,which can assist in identifying potential problems along a supply chain,for example. Other information that can be stored includes informationrelating to how many times specific tags were scanned prior to a sale,which can be used to analyze purchaser preferences. If the tags areapplied to identification or access cards, the information stored in thetag's database record can include the location and/or time at which thetag was scanned. This information can be used to track access to securedlocations, for example.

Information Coding in Dendritic Structures

A variety of different methods can be used to code and de-codeinformation in/from dendritic structures. In general, these methods takeadvantage of the complex, stochastic physical morphology of thestructures to code information. In other words, the information storedin a dendritic structure is represented by the structure's complexphysical features, which are interrogated (for de-coding purposes) at aparticular level of granularity or magnification. Multiple physicalfeatures can be measured and combined to enable the coding ofinformation in different radixes or bases. In general, because thedendritic structures disclosed herein have a high degree of structuralcomplexity and variation, each structure can, in principle, representone of a very large number of different possible values. This makes thestructures ideal for security applications in which the structuresrepresent large key values for, e.g., identification and/orcryptographic purposes.

This portion of the disclosure will first discuss various aspects offractals and general information coding in fractals, and then discussmethods for encoding and de-coding information in the dendriticstructures disclosed herein. It should be appreciated that the methodsdisclosed can be performed by any of the systems disclosed in theforegoing portions of this application.

(a) Fractal Dimension

Dendritic patterns all share the property of self-similarity atdifferent magnifications. Zooming in on a section of the pattern revealsa shape that looks very much like the form of the entire object. Inmathematics, this type of pattern is known as a fractal and ischaracterized by a “fractal dimension”, a number that is related to howthe pattern fills the space in which it forms.

To understand the term fractal dimension, we first have to consider howto calculate the dimension of an object. FIGS. 48A-C show threedifferent objects, respectively—a line, a square, and a cube—withtopological dimensions of 1, 2, and 3 respectively (i.e., a line is1-dimensional, a square is 2-dimensional, and a cube is 3-dimensional).Each object can be broken into smaller parts, each of which is similarto the original. This is the simplest way to illustrate the concept ofself-similarity. For example, the line in FIG. 48A can be broken into 4smaller lines. Each of these smaller lines is similar to the originalline, but they are all ¼ scale. In FIG. 48B, the square can be brokeninto smaller pieces, each of which is ¼ the size of the original. Ittakes 16 of the smaller pieces to create the original. In FIG. 48C, thecube can be broken down into smaller cubes of ¼ the size of theoriginal. It takes 64 of these smaller cubes to create the originalcube.

The mathematical pattern which arises from this is:

-   -   4=4¹    -   16=4²    -   64=4³

This gives us the equation:

N=S ^(D)  [1]

where N is the number of self-similar pieces that go into the fullobject, S is the scale to which the smaller pieces compare to the fullone (e.g., the edge of each small square above is ¼ that of the largesquare so S=4), and D is the dimension (e.g., D=2 in the case of thesquare). These results are somewhat obvious for the simple shapes above,but can be generalized for any fractal that includes self-similarelements by calculating the Hausdorff-Besicovitch or fractal dimensionby solving for D in the previous equation:

D=log N/log S  [2]

A classic example illustrating the fractal dimension is the Koch Curve.This is a regular fractal structure in which each line is split intothree equal parts (S=3) and the middle section becomes an “upside-downV” or chevron with sides the same length as the other fractionalsegments so that we have four segments (N=4), as shown in FIG. 49A. Thefractal dimension D of this shape is log 4/log 3=1.26 which is greaterthan the topological dimension of a line (D=1).

We can continue making each line segment into such a shape indefinitelyto create more complex structures. FIG. 49B shows how the secondgeneration of this fractal is formed. The second generation can beconsidered in two ways. There are now 16 line segments (N=16) but S=9 aseach segment is 1/9 of the original so D=log 16/log 9=1.26, the same asthe first generation (as it should be since this is a fractal). Theother approach is to consider that the second generation is made up of 4copies of the first generation at ⅓ scale (each with D=1.26). This givesthe fractal dimension of the entire structure as log 4/log 3=1.26, thesame as before. This is an excellent illustration of self-similarity andthat each component has the same fractal dimension as the whole. Notethat at higher scale factors, the total (topological) length of thecurve increases but it still fits within the length of the originalline. If the length of the original line was 1 unit, the first Kochcurve will have a total length of 4×⅓=1.33 units and the secondgeneration will have a length of 16× 1/9=42× 1/32=1.78 units.

Continuing, the third generation would contain 64× 1/27=43× 1/33=2.37units. FIG. 49C shows the Koch curve after many generations and it isclear that the level of detail at this scale factor and the overalllength of the curve are both quite large. As expected, this completestructure and all the self-similar elements which make it up also have afractal dimension of 1.26, even though it is much more complex inappearance than the previous examples.

Generalizing, the length L_(n) of the Koch curve is given by

L _(n)=( 4/3)^(n)  [3]

where n is the number of generations. For n=10, L_(n)=17.8 units but forn=100, L_(n) becomes large at over three billion units, even though inall cases the entire pattern fits within a length of 1 unit. Note thatif we went to an infinite number of iterations, the fractal dimensionwould still be 1.26 and but the overall length of the curve would beinfinite and it would still fit within a length of one unit. Thisability to fit a great deal of fine structure in a very small space isone of the most interesting characteristics of fractals.

A similarly simple structure is the Vicsek fractal which is in some wayscloser to the pattern of a dendritic structure in that it containsconstantly branching, albeit highly regular, structures. Representationsof the 1st, 2nd, and 3rd generations of the Vicsek fractal are shown inFIG. 50.

As is evident from FIG. 50, the “segments” are the squares which make upeach cross so that N=5 at a scale of S=3, and D=log 5/log 3=1.46. Aninteresting characteristic of this structure is that at highergenerations, n, of the fractal, the total area decreases as ( 5/9)^(n)but the perimeter increases as 4( 5/3)^(n) so that in the limit the areais zero but the perimeter is infinite.

(b) Information Representation

Each self-similar unit in a fractal can be used to represent informationif it is modified in some way, either deliberately or naturally, toallow subsequent determination of its state.

This is so, even in the relatively simple Koch curve where binaryinformation can be represented by, for example, the direction (up ordown) of the central chevron, as illustrated in FIG. 51.

In FIG. 51, the two elements have the same fractal dimension (log 4/log3) but they are clearly different and therefore are easy to “read” as a0 or a 1. Similarly, information may be encoded in the Vicsek fractal bythe alteration of one or more of the square elements in each cross,e.g., the center square could be white or black with the remainingsquares taking the opposite color to represent 0 and 1. Of course,higher order (greater than binary) number representation is alsopossible by using alterations in more than one element in each similarunit. In the case of the Vicsek fractal, white/black coding can be usedin all five squares of each cross; alternatively, a range of color codescan be used in one or more of the five squares of each cross torepresent numbers.

The processes which cause the modifications to the elements can bedeliberate, e.g., deliberate alteration of one or more units to encode aparticular number that is specified ahead of time, or such alterationscan be be random, e.g., caused by a stochastic process that sets theseconfigurations, and therefore the number associated with them, duringthe formation of the fractal. The alteration of the structure duringformation by “natural” processes is a very important aspect forinformation security applications, provided such natural processes arecapable of creating a vast quantity of unique numbers, each of which canbe mapped to a single entity (physical or virtual) in a database.

The number of self-similar units that can be used to representinformation will depend on the magnification employed—the higher themagnification, the more self-similar “information units” that can beresolved and read. For every generation of the fractal, n, the number ofinformation units, u_(n), is given by

u _(n) =N ₁ ^(n) /N ₁ =N ₁ ^(n-1)  [4]

where N₁ is the number of segments in the first generation self-similarelement (N₁=4 for the Koch curve, N₁=5 for the Vicsek fractal). N isrelated to the initial scale S₁ by

N ₁ =S ₁ ^(D)  [5]

so that

u _(n) =S ₁ ^(D(n-1))  [6]

In terms of scale, n can be written as log S_(n)/log S₁, where S_(n) isthe scale at generation n, which leads to

u _(n) =S ₁ ^(D((log S) ^(n) ^(/log S) ¹ ⁾⁻¹⁾  [7]

This can be re-written as

$\begin{matrix}\begin{matrix}{{\log \mspace{11mu} u_{n}} = {\log \mspace{11mu} S_{1}^{D{({{({\log \mspace{11mu} {S_{n}/\log}\mspace{11mu} S_{1}})} - 1})}}}} \\{= {{D\left( {\left( {\log \mspace{11mu} {S_{n}/\log}\mspace{11mu} S_{1}} \right) - 1} \right)}\log \mspace{11mu} S_{1}}} \\{= {D\left( {\log \mspace{11mu} {S_{n}/S_{1}}} \right)}}\end{matrix} & \lbrack 8\rbrack\end{matrix}$

Since the magnification M which allows us to resolve the informationunits at generation n is merely the scale ratio S_(n)/S₁, we obtain thesimple relationship

u _(n) =M ^(D)  [9]

If the information units are examined for binary information, in whichtwo distinct states are read in each unit (as in the example of the Kochcurve above), the number of unique integers or “capacity” we can obtainfrom the n-th generation of a pattern, I_(n), is

I _(n)=2^(u) ^(n)   [10]

The effect of this relationship is illustrated in the plots of FIGS.52A-F. Specifically, FIGS. 52A and 52B are plots of u_(n) (informationunits) and 2^(u) ^(n) (capacity) vs. M for the Koch fractal (D=1.26),FIGS. 52C and 52D are plots of u_(n) and 2^(u) ^(n) vs. M for the Vicsekfractal (D=1.46), and FIGS. 52E and 52F are plots of u_(n) and 2^(u)^(n) vs. M for a dendritic structure with D=1.7 (a typical value for anatural dendritic or tree-like structure).

A number of interesting aspects of the use of fractals for informationrepresentation may be observed in these plots. Both the number of unitsand the capacity increase substantially with magnification and they alsoincrease with fractal dimension, the latter outcome being due to anincrease in the effective information density of the pattern. The binarycapacity can be vast for reasonable values of both D and M. For example,in the case of a dendritic structure with D=1.7, a magnification of 10×gives a capacity of 10¹⁵ (compared to around 3×10⁵ and 6×10⁸ for thelower fractal dimension Koch and Vicsek structures, respectively);doubling the magnification to 20× results in a resolution that puts thepotential capacity for the dendritic structure in excess of 10⁴⁹. To putthis in perspective, if we increased M to a still modest 27× for thedendritic structure, the potential capacity would equal 10⁸¹ which isthought to be the total number of atoms in the universe.

The capacity of fractal patterns such as dendritic structures to storeinformation becomes vastly larger still if we consider a coding schemethat has more than two identifiable states, i.e., larger than base 2. Ascheme in which we can resolve B individual states would give aninformation capacity of

I _(n) =B ^(u) ^(n)   [11]

The plots in FIGS. 53A and 53B below show the capacity, I_(n), vs.magnification M (from 1 to 10 in FIG. 53A and from 1 to 25 in FIG. 53B)for a pattern with D=1.7 and B=2 (curves 5302 and 5312), 4 (curves 5304and 5314), 8 (curves 5306 and 5316), and 16 (curves 5308 and 5318). At amagnification of 10, the patterns yield a capacity of approximately10¹⁵, 10³⁰, 10⁴⁵, and 10⁶⁰ integers for B=2, 4, 8, and 16, respectively,demonstrating the huge growth in capacity for increasing base. For M=25,the potential capacity rises greatly to around 10⁷¹, 10¹⁴³, 10²¹⁴, and102⁸⁶ states for B=2, 4, 8, and 16, respectively.

(c) Dendritic Fractals

The dendritic structures disclosed herein for use in securityapplications are fractal in nature but the fundamental differencebetween these and the Koch and Vicsek examples is that the dendriticstructures are formed by processes that have a stochastic character.This means that the fractal dimension is preserved at highermagnification as before, but the precise shape of each self-similarelement is unique and random. Accordingly, just like the deliberatecoding in the Koch and Vicsek examples discussed above, we can haveunique and random information generation and representation withoutchanging the fractal dimension and. The stochastic modification inherentin dendritic structure growth is of particular utility in securityapplications as the self-assembly that leads to the dendritic form alsoleads to intrinsic random number generation that can later be used inidentification, authentication, and/or encryption.

Since dendritic structures have a degree of irregularity, determinationof the fractal dimension is not as simple as in the case of regularstructures such as the Koch curve or the Vicsek fractal. An estimate ofD can be obtained, however, by providing a scale S and then placing theminimum number, N, of circles of diameter 1/S that are required to coveras much of the pattern as possible. D is then calculated as log N/log S.

To illustrate this, a first dendritic pattern is shown in FIGS. 54A and54B, analyzed with two different values of S (S=2 in FIG. 54A, S=4 inFIG. 54B). A second dendritic pattern is shown in FIGS. 54C and 54D,analyzed with the same values of S (S=2 in FIG. 54C, S=4 in FIG. 54D).In FIG. 54A, two circles do not quite cover the entire pattern, butthree would encompass too much empty space and so we choose N=2+(meaninga little larger than 2) so that D is just larger than 1, which isclearly inaccurate.

In FIG. 54B, taking S=4 gives a much more realistic result as we getreasonable coverage with six circles so that N=6+, giving D=1.3+. Sincethere is much less of the pattern outside the circles in the S=4 case,we may conclude that the result for D is much closer to 1.3 than 1.0.

In FIG. 54C, three circles give reasonable coverage and so D=1.6+. InFIG. 54D, it takes nine circles to cover the pattern more completelywith very little of the pattern left uncovered and so D appears to bequite close to 1.6. Clearly, higher scale provides a better estimate ofD as any pattern could be covered more completely with smaller circles(or squares, for that matter).

This concept is also used in the “box counting” technique discussedabove, which is frequently used to give a measure of D for complexirregular structures. A simplified example of this is given in FIG. 55,in which the more complex dendritic pattern from FIGS. 54C and 54D iscovered in square grids with S=4 and S=16. For the more coarse grid(S=4), all the squares contain at least some of the pattern, i.e., N=16,leading to D=2 which is clearly inaccurate. To attempt to get a morerealistic measure, we only count the large squares that have substantialcontent (at least 50% penetration by the pattern) and this gives N=9.This suggests that D is somewhere in the range 1.6 to 2. In using thefiner grid (S=16), we count a total of N=176 squares with any content(all colored squares below), although 23 of these have minimal content(yellow squares), leaving a lower boundary for N at 153 (pink squares).This suggests that D actually lies around 1.81 to 1.86.

Thus, for any given number of identifiable states (or coding base) B,magnification M, and fractal dimension D (which can be estimated for adendritic pattern using box counting or similar techniques), the numberof unique integers that can be generated/represented by a fractalstructure (or information capacity) In is given as

I _(n) =B ^(M) ^(D)   [12]

This double exponential function is interesting due to the large growthrate it represents. Double exponential functions obviously grow muchfaster than single exponentials but they also grow faster thanfactorials which makes them of significant interest in fields where verylarge random numbers are generated. In addition to applications whichuse a large number of unique “tags” for identification andanti-counterfeiting purposes, large random number generation is used inthe field of cryptography, and the dendritic structures disclosed hereincan be used to supply unique numbers for keys and ciphers.

In considering the selection of coding base, the ability for theinformation system to perform unambiguous differentiation of states isimportant. Binary coding is the simplest but quaternary (B=4) is areasonable choice in many systems (and one which natural systems such asDNA frequently use). For dendritic structures with D=1.5 (curves 5602and 5612), 1.6 (curves 5604 and 5614), 1.7 (curves 5606 and 5616), and1.8 (curves 5608 and 5618), FIGS. 56A and 56B show plots of capacity vs.magnification for quaternary coding (magnification from 1 to 10 in FIG.56A, and from 1 to 25 in FIG. 56B).

At a magnification of 10, the dendritic structures yield a capacity ofapproximately 10¹⁹, 10²⁴, 10³⁰, and 10³⁸ states for D=1.5, 1.6, 1.7, and1.8, respectively. For M=25, the potential capacity rises to around10⁷⁵, 10¹⁰⁴, 10¹⁴³, and 10¹⁹⁸ states for D=1.5, 1.6, 1.7, and 1.8,respectively. The quantities of unique numbers produced at highermagnifications are well beyond the needs of any current or envisionedfuture item database and are therefore well above the requirements ofany tagging system, although they could certainly be of considerableutility in cryptographic systems as discussed above.

(d) Information Coding and De-Coding in Dendritic Structures

The complex, constantly branching structures of dendritic fractalsreadily offer high information capacity through their relatively highfractal dimension (D=1.5 to 1.7 is typical of natural dendriticstructures) and their potential for a high coding base B. Dendriticstructures typically have features that lend themselves to quaternary orhigher radix coding (e.g., octal or even hexadecimal). For example,considering the dendritic structure pattern of FIG. 57A, the informationunit circled and shown in an expanded view in FIG. 57B has severaldimensions that can be utilized to produce readable states that can inturn be used to code numerical values. These include, for example: thelength L_(A) of segment A from branching point C; the length L_(B) ofsegment B from branching point C, the angle θ_(AC) of segment A withrespect to the segment that terminates at C; the angle θ_(BC) of segmentB with respect to the segment at terminates at C; and the distance andbearing (R_(C), θ_(C)) of branching point C from a fiducial mark F. The“stick-like” pattern in FIG. 57A, which facilitates geometricmeasurements, can be generated from the image of a natural dendriticstructure via the use of “thinning” functions which replace the varyingwidths of trunks, branches, and twigs with uniform lines that correspondto the mid-lines of the original elements, as discussed previously.

In a quaternary coding scheme, readable states such as key dimensions(absolute measurements) or key dimensional relationships (relativemeasurements) can be used to generate the numbers 0, 1, 2, and 3 foreach information unit. As an example, for a structure similar to thatshown in FIG. 57A, the following relative dimensional relationships canbe used to implement a quaternary coding scheme:

if L_(A)>L_(B) and θ_(AC)>θ_(BC) then the information unit represents avalue of 0

if L_(A)<L_(B) and θ_(AC)>θ_(BC) then the information unit represents avalue of 1

if L_(A)>L_(B) and θ_(AC)<θ_(BC) then the information unit represents avalue of 2

if L_(A)<L_(B) and θ_(AC)<θ_(BC) then the information unit represents avalue of 3

For the specific information unit circled in FIG. 57A, L_(A)<L_(B) andθ_(AC)<θ_(BC) so the resulting integer is 3 by the above coding scheme.

Using dimensional relationships rather than absolute dimensions may helpto reduce the effects of measurement error. Where measurements giveambiguous results, e.g., L_(A) appears to be very close to L_(B), a(further) conditional metric can be used. For example, if L_(A)≈L_(B)then a third (random) variable could be employed as a tie-breaker.

Absolute measurements have the advantage of providing a high radix froma single segment, e.g., angle of segment A to the segment thatterminates at C (θ_(AC)) alone may generate the numbers 0, 1, 2, and 3by providing ranges as follows:

if θ₀<θ_(AC)<θ_(0*) then the information unit represents a value of 0

if θ₁<θ_(AC)<θ_(1*) then the information unit represents a value of 1

if θ₂<θ_(AC)<θ_(2*) then the information unit represents a value of 2

if θ₃<θ_(AC)<θ_(3*) then the information unit represents a value of 3

The non-overlapping angular ranges θ₀ to θ_(0*), θ₁ to θ_(1*), etc., arethe readable states and are chosen to give equal probability of theresult being 0, 1, etc. Proper range selection is based on accurateknowledge of the formation processes for dendritic structures asincorrect ranges could possibly introduce a “bias” into the result. Forexample, if the formation process favored a particular range of anglesthen one number would be generated more often than the others whichbiases random number generation.

To obtain a higher radix coding from a single measurement, moremeasurement ranges/readable states are used. For example, octal codingwould require eight non-overlapping angular ranges, representing thenumbers 0 through 7. In principle, the number of distinct ranges thatcan be used is limited only by measurement errors associated withaccurate determination of values of the parameter (e.g., θ_(AC)) usedfor coding.

If a similar four range/state methodology was used for anotherparameter, e.g., θ_(BC), a separate radix 4 result can be obtained. Thetwo radix 4 measurements can also be combined to implement radix 16(e.g., hexadecimal) coding without increasing measurement precisionbeyond four ranges per measured parameter. As an example, the followingcoding scheme could be used:

if θ₀<θ_(AC)<θ_(0*) and θ_(0†)<θ_(BC)<θ_(0‡) then the information unitrepresents a value of 0

if θ₁<θ_(AC)<θ_(1*) and θ_(0†)<θ_(BC)<θ_(0‡) then the information unitrepresents a value of 1

if θ₂<θ_(AC)<θ_(2*) and θ_(0†)<θ_(BC)<θ_(0‡) then the information unitrepresents a value of 2

if θ₃<θ_(AC)<θ_(3*) and θ_(0†)<θ_(BC)<θ_(0‡) then the information unitrepresents a value of 3

if θ₀<θ_(AC)<θ_(0*) and θ_(1†)<θ_(BC)<θ_(1‡) then the information unitrepresents a value of 4

if θ₁<θ_(AC)<θ_(1*) and θ_(1†)<θ_(BC)<θ_(1‡) then the information unitrepresents a value of 5

if θ₂<θ_(AC)<θ_(2*) and θ_(1†)<θ_(BC)<θ_(1‡) then the information unitrepresents a value of 6

if θ₃<θ_(AC)<θ_(3*) and θ_(1†)<θ_(BC)<θ_(1‡) then the information unitrepresents a value of 7

if θ₀<θ_(AC)<θ_(0*) and θ_(2†)<θ_(BC)<θ_(2‡) then the information unitrepresents a value of 8

if θ₁<θ_(AC)<θ_(1*) and θ_(2†)<θ_(BC)<θ_(2‡) then the information unitrepresents a value of 9

if θ₂<θ_(AC)<θ_(2*) and θ_(2†)<θ_(BC)<θ_(2‡) then the information unitrepresents a value of A

if θ₃<θ_(AC)<θ_(3*) and θ_(2†)<θ_(BC)<θ_(2‡) then the information unitrepresents a value of B

if θ₀<θ_(AC)<θ_(0*) and θ_(3†)<θ_(BC)<θ_(3‡) then the information unitrepresents a value of C

if θ₁<θ_(AC)<θ_(1*) and θ_(3†)<θ_(BC)<θ_(3‡) then the information unitrepresents a value of D

if θ₂<θ_(AC)<θ_(2*) and θ_(3†)<θ_(BC)<θ_(‡) then the information unitrepresents a value of E

if θ₃<θ_(AC)<θ_(3*) and θ_(3†)<θ_(BC)<θ_(3‡) then the information unitrepresents a value of F

The non-overlapping angular ranges θ₀ to θ_(0*), θ₁ to θ_(1*), etc., arethe readable states for θ_(AC), and θ_(0†) to θ_(0‡), θ_(1†) to θ_(1‡),etc. are the readable states for θ_(BC). These are generally chosen toprovide an unbiased result for each parameter. For structures in which alack of true randomness during formation for any parameter is observed(e.g., due to favored states caused by the formation process), otherparameters can be incorporated into the coding scheme.

If length is used as the coding measurement, four length ranges forL_(A) would yield a radix 4 result but combining four length ranges forboth L_(A) and L_(B) (as for θ_(AC) and θ_(BC) above) would again yielda radix 16 (numbers 0 through F) coding scheme. Generalizing, the radixor coding base B can be represented by

B=R ^(P)  [13]

where R is the number of readable states chosen, and P is the number ofparameters measured, assuming that each parameter has the same number ofreadable states. For R=4 and P=1 (a single parameter measured), B=4,giving us quaternary coding. Two parameters gives B=16 (hexadecimal),three gives B=64, four gives B=256, etc. Combining this with theexpression for information capacity gives

I _(n)=(R ^(P))^(M) ^(D)   [14]

This triple exponential function has an extraordinarily high growthrate. For the earlier simple Koch curve example at 3× magnification, R=2(an “up” or “down” chevron in each structure), P=1 (measurement of oneparameter−the position of the chevron), M=3 (showing four self-similarstructures), and D=log 4/log 3, so that R^(P)=2, M^(D)=4, so thecapacity is a mere 16 integers. For a dendritic structure with a fractaldimension of 1.7, measuring two variables with four readable states at10× magnification, (i.e., R=4, P=2, M=10, and D=1.7), R^(P)=16,M^(D)=50.12, and I_(n)=2.2×10⁶⁰. Another illustration of the growth ofthe function is given in Table 2 below, in which the three fractalsdiscussed above are compared at a magnification of 10. In Table 2, twosimple Vicsek coding schemes are included: Vicsek₁ in which the centersquare in each cross is either black or white; and Vicsek₅ which allowsany single square in each cross to be black with the rest being white,leading to 5 readable states in 1 parameter.

TABLE 2 Fractal R P M D I_(n) Koch 2 1 10 1.26   3 × 10⁵ Vicsek₁ 2 1 101.46 4.8 × 10⁸ Vicsek₅ 5 1 10 1.46 1.4 × 10²⁰ Dendrite 4 2 10 1.7 2.2 ×10⁶⁰

To show the effect of the number of parameters measured, FIG. 58 is aplot of information capacity I_(n) vs. parameters P for a dendriticstructure with D=1.7 and R=4 at M=10. Additional parameters P can arisefrom more complex patterns in each information unit (e.g., more branchesand consequently higher fractal dimension) or from the use ofmeasurements that are external to the information unit such as range andbearing from a fiducial mark as shown in FIG. 57A.

Where the readable states are not the same for each measured parameterin an information unit, the equation for the coding base B can begeneralized as

B=R ₁ ×R ₂ ×R ₃ × . . . ×R _(P)=Π_(t=1) ^(P) R _(i)  [15]

where R_(i) is the number of readable states for parameter i. This leadsto a more general expression for information capacity:

I _(n)=(Π_(i=1) ^(P) R _(i))^(M) ^(D)   [16]

Equation (16) assumes that the information base is the same for eachinformation unit, a reasonable assumption since these are self-similarand therefore contain elements that will yield similar readable statesand parameters. Table 3 below gives an example of five coding schemeswith P ranging from 1 to 4 and R values of 2 and 4, I_(n) beingcalculated for M=10 and D=1.7. Again, it is obvious from these sampleresults that increasing P and R cause a very large increase in capacity.

TABLE 3 Scheme R₁ R₂ R₃ R₄ P M D I_(n) a 2 — — — 1 10 1.7 1.2 × 10¹⁵ b 22 — — 2 10 1.7 1.5 × 10³⁰ c 2 2 4 — 3 10 1.7 2.2 × 10⁶⁰ d 2 2 4 4 4 101.7 3.3 × 10⁹⁰ e 4 4 4 4 4 10 1.7  5.0 × 10¹²⁰

Referring again to Equation (14), the information capacity I_(n) for aparticular coding scheme can be expressed as a triple exponentialfunction in terms of the number of readable states R, the number ofparameters P, the magnification M at which images of the dendriticstructures are obtained, and the fractal dimension D, where the numberof readable states is assumed to be the same for each parameter. In someembodiments, values for each of R, P, M, and D can be chosen so thatparticular dendritic structures are analyzed at a particular informationdensity level. That is, values for each of R, P, M, and D are determined(i.e., either automatically by system software or via user-selected or-entered preferences) prior to analyzing the dendritic structures tocontrol the number of unique integers that each pattern is assumed to becapable of representing.

For example, for certain applications involving relatively low securitylevels (e.g., “minimum security” applications) or in a “first pass” of amulti-level security screening procedure, values for each of R, P, M,and D can be chosen to yield a relatively low information density level.Thus, each dendritic structure analyzed is assumed to represent only oneof a relatively small set of possible integers. In these applications,scanning and analysis of the dendritic structure is frequently performedat high-speed for purposes of rapidly and generally assessing theinformation represented by the structure. As an example, a “lowsecurity” or “rapid scanning” first analysis can be performed todetermine information such as which one of several categories thedendritic structure represents, or whether the dendritic structurecorresponds to a binary “pass” or “fail” classification. In applicationswhere the number of possible classifications, states, or outcomes isrelatively limited, a relatively low information density can beadvantageous, as it enables more rapid screening (due to the lessdetailed analysis involved), and can also allow for improved errortolerance, as the integer represented by the dendritic structure istypically not as sensitive to small variations in the morphology of thestructure.

For applications involving higher security levels (e.g., “mediumsecurity” or “maximum security” applications) or in later passes ofmulti-level screening procedures, values for each of R, P, M, and D canbe chosen to yield a relatively higher information density levels.Although analysis of dendritic structures is typically slower at higherinformation density levels, the reduced speed is generally warranted bythe increased security requirements. As an example, a higher informationdensity can be used in forensic applications, or in a second screeningstep of a multi-level screening procedure where dendritic structureswhich have first been pre-classified in an initial screening step (e.g.,at lower information density) are then analyzed at a higher informationdensity level to elucidate finer differences between the structures,thereby further classifying the structures.

As explained above, values for each of R, P, M, and D can be chosen toyield a selected information density level (i.e., the number of possiblestates represented by dendritic structures that are analyzed) either byuser-selected or -entered preferences, or, in some embodiments,automatically using stored system settings. In certain embodiments, thesystems disclosed herein can be configured to retrieve stored values ofR, P, M, and D based on information about the particular applicationinvolved. For example, a user of the system can enter applicationinformation or select from a list of available applications on a userinterface. With this information, the system can then determineappropriate values of R, P, M, and D to set the information density. Inthe system's storage unit, appropriate values of R, P, M, and D can bestored in records associated with particular applications.Alternatively, or in addition, the system can first determine anappropriate security level associated with a particular application, andthen retrieve stored values of R, P, M, and D that are commensurate withthe security level. For applications involving multiple security levels(such as multi-level scanning procedures), the system can adjust thevalues of R, P, M, and D (e.g., by retrieving new sets of theseparameters for each successive step in the procedure) during thescanning and analysis operation.

The measurement of geometric features to produce unique parametric setscan be achieved via software operating on a captured image of thepattern. In some embodiments, a more “Cartesian” approach can be appliedto the generation and reading of information which can lead to fasterand more efficient computation, as the input to the computer will mostlikely be from a digital camera which uses a sensor that captures imagesin the form of an X-Y array of values. If this arrayed data can beanalyzed more directly, it potentially saves software conversion andanalysis steps, reducing overall processing time.

Cartesian coding shares some features in common with box countingmethods in that a grid is applied over the pattern and the boxes whichcontain any part of the pattern are counted, as shown for a simpledendritic structure in FIG. 59. For the structure in FIG. 59, it takes24 boxes at ⅛th scale to encompass the solid lines in the pattern and sowe can estimate the fractal dimension as log 24/log 8=1.53.

To code the pattern of solid lines using the grid, the positions of theoccupied boxes on the grid space are recorded. If the lower left greenbox is (1,1) in this example, the dendritic structure occupies thefollowing set of coordinates (ordered by row):

(4,1),

(1,2), (4,2),

(1,3), (2,3), (3,3), (4,3), (5,3),

(2,4), (3,4), (4,4),

(2,5), (4,5), (5,5), (6,5), (7,5),

(4,6), (5,6), (6,6),

(4,7), (6,7), (7,7), (8,7),

(6,8)

This set of 24 coordinates forms the basis for the generation of theinteger associated with the pattern. In a digital computation scheme,the coordinates can correspond to the addresses of the data in thecomputer memory. If the pattern is even slightly different, e.g., thegray solid line in (4,1) takes up the dashed line position and extendsinto blue box (5,2) instead, the set of coordinates changes to:

(1,2), (4,2), (5,2),

(1,3), (2,3), (3,3), (4,3), (5,3),

(2,4), (3,4), (4,4),

(2,5), (4,5), (5,5), (6,5), (7,5),

(4,6), (5,6), (6,6),

(4,7), (6,7), (7,7), (8,7),

(6,8)

A different integer is generated from this set of coordinates.

If the scale of the box grid is given by S_(G) (and the total number ofgrid squares/locations in a square array is S_(G) ²), then the totalnumber of coordinates in the set C is simply

C=S _(G) ^(D)  [17]

and the ratio of the number of pattern squares to grid locations G is

S _(G) ^(D) /G=S _(G) ^(D/S) _(G) ² =S _(G) ^(D-2)  [18]

A finer grid captures more detail in the pattern and therefore generateshigher information content. This results in a larger coordinate set butthe ratio of the number of pattern coordinates to the total number ofgrid locations decreases greatly as the latter increases, as shown inFIG. 60. As demonstrated with the Vicsek fractal discussed above, thisreduction in fractional area with increasing scale is an importantcharacteristic of fractals.

A practical limit of this grid coding technique may be the physicalresolution of the camera sensor that is used to capture the image of thepattern, i.e., how many pixels the imaging element has. Even relativelyinexpensive digital cameras, such as those found in cell phones, havesensors with multi-megapixel capability so a grid of several thousand byseveral thousand boxes is possible. For G=3000×3000=9 million pixelsquare array covering a pattern that has D=1.7, the number ofcoordinates that will describe the pattern C=3000^(1.7)=8.15×10⁵.Different patterns will, of course, have different individualcoordinates but the number of coordinates in the set will be about equalfor patterns with the same fractal dimension.

When the resolution is large, the number of coordinates that uniquelyrepresents the pattern can be considerable but it is the possiblevariations of these coordinates that creates a very large number ofpossible sets which in turn can be used to generate unique integers.Consider the simple case with a non-branching structure in which eachcoordinate could take on 2 possible values at each point in the pattern,i.e., (x_(g) ⁺, y_(g) ⁺) or (x_(g) ⁻, y_(g) ⁻) at location g where1<g<C, as shown in FIG. 61. This binary single branch structure yields2^(C) possible outcomes. For the case of a pattern which has 24coordinates, if each of these can take on two values, there are 2²⁴possible outcomes, close to 17 million variations in the coordinate set.Considering the nine megapixel example in which C=8.15×10⁵, there couldbe over 10^(245,000) possible variations. This is obviously a hugenumber but is considerably smaller than the possible number ofvariations if every location the 3000×3000 grid could take on a binaryvalue, i.e., C=9×10⁶ which gives 10^(2,710,000) possible variations.

The binary non-branching/single branch constraint is, of course, highlyconservative as each of the coordinates in the set can realisticallytake on more than two values, depending upon whether the pattern hascontinued, branched, or terminated at any location in the grid. Thefirst two options also have additional possibilities associated withthem, as shown in FIG. 62.

This suggests that a k-ary (rather than binary) structure should beconsidered, where k could reasonably be 6. In a k-ary structure, we havek^(C) possible variations so that the nine megapixel example would yieldan astonishing 6^(815,000) or more than 10^(634,000) possible values.

Various criteria can be used to determine whether a particular box in agrid structure is occupied by a portion of a dendritic structure. Insome embodiments, the box is occupied if even one pixel corresponding tothe box overlaps with a portion of the dendritic structure. In certainembodiments, the box is occupied only if the box's fill factor (e.g.,the ratio of the number of box pixels that overlap with a portion of thedendritic structure to the total number of box pixels) exceeds athreshold value. For example, the threshold value can be 50% or more(e.g., 60% or more, 70% or more, 80% or more).

In general, for the Cartesian encoding approach, the information densityIn is a function of the number of structural options k, the total numberof grid locations or boxes G, and the fractal dimension D, according to:

I _(n) =k ^(G) ^(D/2)   [19]

In some embodiments, values for each of G and D can be chosen so thatparticular dendritic structures are analyzed at a particular informationdensity level. That is, values for each of G and D are determined (i.e.,either automatically by system software or via user-selected or -enteredpreferences) prior to analyzing the dendritic structures to control thenumber of unique integers that each pattern is assumed to be capable ofrepresenting.

For example, as discussed above, in low security applications (or in theinitial step of a multi-step screening procedure), dendritic structurescan be analyzed at a relatively low information density by selectingsuitable values for G and D such that the dendritic structures analyzedare assumed to represent one of only a relatively small number ofintegers. Scanning and analyzing dendritic structures at low informationdensities can be advantageous because it can generally be performed morerapidly than analyses at higher information densities, and may alsopermit higher error tolerances as the integer represented by a givendendritic structure can be less strongly dependent on small structuralvariations.

In higher security applications, or in later stages of a multi-stepscanning procedure, dendritic structures can be analyzed at higherinformation densities by suitably choosing different values of G and D.To implement multi-step analysis procedures, the values of D and G canbe adjusted between steps as discussed above.

The previous analysis was based on a Cartesian approach but we couldalso use a “polar” method in which the pattern is divided by a series ofconcentric circles as shown in FIG. 63. There are several ways that thiscan be used to extract information from the pattern. In someembodiments, sectors are formed over the pattern by placing lines thatradiate from the center with angles between them of 360°/F, where F isthe desired number of sectors per ring. The sectors which contain partof the pattern are then logged as in the Cartesian approach above butthis time with radius and angle (r, φ) defining each sector. The maindifference between Cartesian and polar methods is that the boxes aretypically all the same size in the former whereas the sector area A_(s)in the polar case will be determined by the difference in the squares ofeach successive radius.

If the radii follow a simple progression such as hr₀, where r₀ is theradius of the smallest circle and h=1, 2, 3, etc. up to the number ofthe last circle, then the increase in sector area ΔA_(s) from one radiusto the next is given as

ΔA _(S) =πr ₀ ²·2(h−1)/F  [20]

The resolution will therefore decrease from the center to the edge ofthe pattern unless the larger sectors are further divided to sub-sectorsthat keep the area of each cell equal throughout the polar grid. Sincethe smallest cell area A₀=πr₀ ²/F, the grid can be standardized to thisby using the fact that the area of each sector at radius hr₀ is

A _(S,h) =πr ₀ ²(2h−1)/F  [21]

so that the ratio of this sector area to the standard (minimum) area is

A _(S,h) /A ₀=2h−1  [22]

This means that each sector created by the choice of F must be splitinto 2h−1 sub-sectors, each having area A₀. For example, in the ringbetween the first and second circles (h=2), the main sectors must bedivided into 3 sub-segments; sectors in the h=3 ring will be dividedinto 5 sub-sectors, the h=4 ring sectors will have 7 sub-sectors, and soon. The placement of the sub-sectors is naturally dictated by thepositions of the lines which define the sectors so that the sub-sector“grids” may be standardized; if the sub-sectors were not aligned to thesectors, the polar grid could be different each time, with differentalignments of the sub-sectors in each ring. In terms of angles, for theexample of F=120 leading to sectors of angular width 3°, the sub-sectorsin h=2 the ring would have and angular spacing of 3°/3=1°, the h=3ring's sub-sectors would be spaced by 3°/5=0.6°, and so on.Generalizing, the angular spacing/resolution of a sub-sector in ring his given as

Φ_(ss)=360°/(2h−1)F  [23]

The total number of sub-sectors (or addresses), G, available in a polargrid with E circles/discrete radii and F sectors is

G=Σ _(h=1) ^(E)(2h−1)F=E ² F  [24]

For example, if we have E=300 (circles) and F=100 (sectors), we willhave 9 million “pixels” as in the Cartesian example above. The polargrid is more complex than the Cartesian “box” method but does havecertain potential advantages. For example, in the case of a radialdendritic structure (one that has been grown from a central point), apolar grid better fits the shape of the pattern.

An alternative polar approach is to overlay concentric circles as beforeand then record the points where the dendritic structure and the circlesintersect. These points are characterized by simple vectors containingtheir distance r from a fiducial mark (e.g., the center point of thedendritic structure) and angle φ from a baseline, as shown in FIG. 64(the baseline corresponds to the dotted line in the figure). Theresolution of this scheme depends on the spacing of the circles (smallerspacing means more circles which in turn means more intersections) andas long as their radii are discrete, the vectors produced will also bediscrete “samples” of the entire pattern. This technique simplifies themeasurements and reduces the amount of data to be handled in the readingscheme.

(e) Dendritic Structure Verification

In both the geometric and Cartesian approaches discussed above, thesystems disclosed herein can be configured to verify the integrity ofthe information (e.g., the integer value) represented by a particulardendritic structure by determining the structure's fractal dimension Dunder different conditions. For a given dendritic structure, the fractaldimension D should be constant, independent of the magnification Matwhich the image of the dendritic structure is obtained, independent ofthe number of pixels in the image (or number of grid points G) used foranalysis, and independent of the location within the dendritic structureat which D is determined. By determining D for a given structure atdifferent magnifications and/or in images with different numbers ofpixels or grid points for analysis and/or at different locations withinthe structure, and comparing the values of D obtained under thesevarious conditions, the integrity of the information represented by thedendritic structure can be verified (e.g., if the values of D agree towithin a specified tolerance value). If the values of D do not agree,then corruption of the dendritic structure has likely occurred.

All dendritic structures grown under similar conditions should also havethe same fractal dimension D. Thus, for a given dendritic structure,values of D determined at different magnifications, at differentlocations, and/or using different numbers of image pixels or gridpoints, can be compared by the systems disclosed herein to referenceinformation for the type of dendritic structure being analyzed todetermine whether D is within an acceptable range of values. Even ifmultiple values of D determined for a particular dendritic structureagree with one another, they may still fall outside an acceptable rangeof values for the particular type of dendritic structure being analyzed,indicating that the structure has likely been compromised or does notcorrespond to a dendritic structure of the expected type. In someembodiments, individual D values for a particular structure can each becompared to a reference range to assess structure corruption. In certainembodiments, particularly where multiple D values are determined andagree for a particular structure, the multiple D values can be averagedand compared to reference range information.

As an additional verification of the integrity of the informationrepresented by a particular dendritic structures, the systems disclosedherein can be configured to use adjacency algorithms to determine howmuch of the spatial region surrounding any particular point in thepattern represented by the dendritic structure should contain additionalportions of the pattern. For example, the systems can be configured topredict, based on the analyzed portions of the dendritic structure, theanticipated pattern represented by other (e.g., adjacent) portions ofthe structure. The additional portions of the actual structure are thencompared to the predicted pattern to determine the extent of the match.If selected system tolerances are violated (e.g., too few adjacentlocations or too many adjacent locations contain an extension of thepattern represented by the actual dendritic structure, based on theexpected pattern), then it is likely that dendritic structure has beencorrupted, and the information it represents as well.

(f) Error Correction

In general, any pattern containing multiple units with severalidentifiable states per unit could be used to generate and representnumbers. For instance, an array of pixels in which each element can berandomly black (e.g., 0) or white (e.g., 1) can be used to generatenumbers; a mere 1000 of such binary pixels would yield 2¹⁰⁰⁰ or about10³⁰¹ possible integers. A nine megapixel binary array could potentiallygive yield 10^(2,710,000) values.

However, there are issues beyond capacity that are relevant to thechoice of coding scheme, chief among them the unambiguous determinationof the numbers that the patterns represent at various points in time andspace. What makes fractal patterns of particular interest forinformation representation is that their structure is predictable at allmagnifications; we know that all information units must have the samefractal dimension and the same general shape, even if they are differentin some way. This predictability of form is important for robustinformation representation as noise in the form of pattern distortions,surface imperfections, material defects, reading errors, etc. can easilycorrupt pattern information.

In the pixel array example at in the previous paragraph, it would beimpossible to know if an element had an incorrect coding via a randomerror as there is no structure to the pattern—random errors in a randompattern are in essence invisible. This is why existing matrix barcodeschemes, essentially 2-dimensional arrays of pixels, such as the QuickResponse or QR code, have substantial error correction coding or ECCbuilt in (typically a sophisticated Reed-Solomon correction) and thissignificantly reduces the information capacity of the pattern.

Fractals do not require extensive extrinsic error correction due totheir intrinsic predictability which allows us to determine if they havebeen corrupted and can even help to correct the problem. In other words,if the form of the shape is known, it is much easier to fill in missingportions or remove extraneous objects.

FIG. 65A is a schematic diagram of a pristine dendritic structure. FIG.65B is a schematic diagram of the same structure as in FIG. 65A, withcertain “damage features” added that lead to measurement noise and/orerrors. In FIG. 65C, the damage features have been identified andlabeled 1-4. Because these features have altered the shape and/ordensity of the pattern at a local level, the fractal dimension in theseregions will have changed and this is the first indication of thepresence of noise.

Considering each error in turn and possible strategies for correction,feature 1 is a gap in two branches which should be continuous. This isapparent due to the alignment of the disembodied sections and the changein the fractal dimension (or increase in the local lacunarity) of thefeature. A “digital repair” is relatively straightforward in this caseby interpolating the missing sections via software and regenerating thenumber associated with the pattern.

Noise features 2 to 4 are additional lines within the pattern but 2 isnot an extension of the existing structure and therefore can be ignored.Feature 3 links two branches which is not allowed in a planar dendriticpattern and so this should be erased. Feature 4 results in a retrograde(backward growing) branch section which also may be flagged as unusual.This last feature illustrates that directionality can be useful in theelimination of spurious features, as a simple or complex pattern that is“going against the grain” of the dendritic structure can be consideredto be an error and ignored in the analysis.

Accordingly, with knowledge of how the dendritic pattern should appeargenerally, it can be relatively straightforward to identify and correctgross errors. More subtle errors, such as point defects in the patternor in the spaces between the features, can be corrected using averagingtechniques, e.g., if most of the pattern surrounding a “white” point is“black”, then the point should also be black and vice-versa.

In the Cartesian or polar coding approaches, the fractal dimension canbe determined and monitored via a box-counting (or related) method toensure integrity for the entire pattern or in specific regions. Theidentification of specific errors can be achieved by the use ofadjacency algorithms which deal with the data at the pixel level. Insuch methods, for any pixel that includes the pattern there will exist anumber of “allowed” adjacent pixels which arise from the pattern'sfractal dimension and the “growth rules” of dendritic structures. If weconsider a 3×3 pixel square with a piece of the pattern (or a portion ofthe thinned pattern) in the central pixel, the number of pixels whichare allowed to also contain part of the pattern, a_(p), is

a _(p) =[S ^(D)−1]  [25]

where [ . . . ] indicates the floor of the function within the brackets(i.e., the result, a_(p), is given in whole pixels). Since the edge ofthe region in the example above has 3 pixels, the scale factor S equals3, so that the number of allowed pixels, a_(p), in the 8 pixels adjacentto the central one for a D=1.5 pattern is 4, and for a D=1.7 pattern is5. Similarly, expanding the surrounding neighborhood to a 5×5 pixelsquare (24 neighboring pixels in all) so that S=5, a D=1.5 pattern hasa_(p)=10 pixels and a D=1.7 pattern has a_(p)=14 pixels. Informationabout the number of allowed pixels can be combined with the dendriticgrowth rules discussed earlier, which forbid gaps, disembodied features,elements which link separate branches, and significant retrogradepattern evolution, to provide a final determination of pattern/imagevalidity.

Another significant source of error is pattern alteration caused by theimage capture process itself. If a camera is used, imagetranslation/rotation, geometric distortion, imperfect focus, etc., canchange the appearance of the image and this can be accounted for in theanalysis. Whereas there are a number of software-based techniques thatmay be used to analyze/recognize distorted patterns, such asscale-invariant feature transform (SIFT) methodologies, simplerapproaches are almost certainly more appropriate in the case ofmanufactured patterns and relatively controlled reading environments.

In some embodiments, fiducial marks with known geometric properties canbe used, which allow the simple and rapid determination of patternposition and orientation, focus/blur, contrast, and other opticaldistortions such as keystone effects caused by the pattern/substratebeing not parallel to the focal plane of the optical system. These markscan be printed on the substrate that contains the information pattern,captured with the same reading system, and the analysis used to correctdistortions in the pattern.

An example of the use of a fiducial marking system is shown in FIGS.66A-D. Three cross-like fiducial marks have been added to a substratethat carries a dendritic pattern, as shown in FIG. 66A. The marks havedimensions and relative positioning that are known to the system. Byanalyzing the positions and dimensions of the fiducial marks in theimage of the dendritic structure, the system can determine when theentire image has been rotated (FIG. 66B), defocused (FIG. 66C), and/orexhibits keystone distortion (FIG. 66D).

In some embodiments, dendritic pattern errors caused by imperfectmanufacturing or severe use environments can be mitigated via the use ofredundancies. As discussed previously, the capacity of a dendriticfractal pattern can be expressed as

I _(n)=(Π_(i=1) ^(P) R _(i))^(M) ^(D) =(Π_(i=1) ^(P) R ^(i))^(u) ^(n)  [26]

The double exponent M^(D) gives the total number of resolvableinformation units in the pattern but it is also possible for us to use asubset of units, u_(n), to generate our unique integers so that thecapacity becomes

I _(n)=(Π_(i=1) ^(P) R _(i))^(u) ^(n) ^(′)  [27]

As long as a high capacity is maintained, not using all units in thepatterns can be a good strategy as it allows certain units to beignored, e.g., those which may have manufacturing defects or areotherwise of poor quality, in the original (newly-formed) pattern. Anumber of units can also be reserved for other purposes, e.g., togenerate a secondary code that is not related to the integer createdfrom the rest of the pattern. For example, in the case of M^(D)=50, 10%of the units can be reserved for redundancy, so that u_(n)′=45. Even ina simple reading scheme where R=2 and P=2, this still allows for thecoding of over 10²⁷ integers.

Additional Aspects and Features

Additional aspects and features of dendritic structures and theirapplications are disclosed, for example, in the following documents, theentire contents of each of which is incorporated herein by reference:PCT Patent Application No. PCT/US2014/024233, filed on Mar. 12, 2014 andpublished as WO 2014/165047; and PCT Patent Application No.PCT/US2014/024557, filed in Mar. 12, 2014 and published as WO2014/165148.

Hardware and Software Implementation

The algorithmic and method steps disclosed herein in connection withcontrolling voltages and other fabrication parameters, obtaining imagesof dendritic tags, analyzing the images, authenticating and identifyingarticles to which such tags are attached, and controlling variousaspects and operating parameters of devices that obtain tag images anddevices that utilize such tags, can be implemented in computer programsusing standard programming techniques. Such programs are designed toexecute on control units, programmable computers, and/or specificallydesigned integrated circuits, each comprising an electronic processor, adata storage system (including memory and/or storage elements), at leastone input device, and least one output device, such as a display orprinter. The program code is applied to input data to perform thefunctions described herein and generate output information, which isapplied to one or more output devices, such as a user interface thatincludes a display device. Each such computer program can be implementedin a high-level procedural or object-oriented programming language, oran assembly or machine language. Furthermore, the language can be acompiled or interpreted language. Each such computer program can bestored on a tangible, computer readable storage medium (e.g., CD ROM ormagnetic diskette) that, when read by a computer or other device, cancause the processor to perform the analysis and control functionsdescribed herein.

OTHER EMBODIMENTS

A number of embodiments have been described. Nevertheless, it will beunderstood that various modifications may be made without departing fromthe spirit and scope of the disclosure. Accordingly, other embodimentsare within the scope of the following claims.

1-104. (canceled)
 105. A system, comprising: a detector configured toobtain at least one image of a dendritic structure; and an electronicprocessor configured so that during operation of the system, theelectronic processor: analyzes the at least one image to identify one ormore features associated with the dendritic structure; and determines anumerical value associated with the dendritic structure based on the oneor more features.
 106. The system of claim 105, wherein the one or morefeatures comprise at least one of: one or more angles between segmentsof the dendritic structure; one or more lengths of segments of thedendritic structure; one or more distances of locations on the dendriticstructure from a reference point; and one or more angles of rotation oflocations on the dendritic structure relative to a reference line. 107.The system of claim 106, wherein the electronic processor is configuredto analyze the at least one image by at least one of the following:determining, for each of the one or more angles, the numerical value bycomparing each of the one or more angles to angular ranges associatedwith each of the one or more angles; determining, for each of the one ormore lengths of segments, the numerical value by comparing each of theone or more lengths of segments to numerical ranges associated with eachof the one or more lengths of segments; determining, for each of the oneor more distances of locations on the dendritic structure, the numericalvalue by comparing each of the one or more distances of locations tonumerical ranges associated with each of the one or more distances oflocations; and determining, for each of the one or more angles ofrotation of locations on the dendritic structure, the numerical value bycomparing each of the one or more angles of rotation of locations on thedendritic structure to angular ranges associated with each of the one ormore angles of rotation of locations on the dendritic structure. 108.The system of claim 105, wherein the electronic processor is configuredto determine the numerical value by determining a binary digitassociated with each of the one or more features.
 109. The system ofclaim 105, wherein the electronic processor is configured to determinethe numerical value by determining a base n digit associated with eachof at least some of the one or more features, wherein n is greater than2.
 110. The system of claim 105, wherein the one or more featurescomprises at least one of multiple angles between segments of thedendritic structure and multiple lengths of segments of the dendriticstructures, and wherein the electronic processor is configured to atleast one of compare values of at least two of the multiple angles todetermine the numerical value and compare values of at least two of themultiple lengths to determine the numerical value.
 111. The system ofclaim 109, wherein the electronic processor is configured to determinethe base n digits associated with at least some of the one or morefeatures by: comparing a value of a first one of the one or morefeatures to a value of a second one of the one or more features; andcomparing a value of a third one of the one or more features to a valueof a fourth one of the one or more features.
 112. The system of claim105, wherein the one or more features comprise a set of coordinatesassociated with a spatial distribution of the dendritic structure on acoordinate system.
 113. The system of claim 112, wherein the electronicprocessor is configured to identify the set of coordinates bydetermining portions of the coordinate system into which the dendriticstructure extends.
 114. The system of claim 105, wherein prior toidentifying the one or more features, the electronic processor isconfigured to: determine a fractal dimension associated with at least aportion of the dendritic structure; identify anomalous features withinthe at least a portion of the dendritic structure based on the fractaldimension; and correct the at least a portion of the dendritic structureto remove the anomalous features.
 115. The system of claim 105, whereinprior to identifying the one or more features, the electronic processoris configured to: identify anomalous segments of the dendritic structurebased on a growth pattern associated with the dendritic structure; andcorrect the dendritic structure by removing the anomalous segments. 116.The system of claim 105, wherein prior to identifying the one or morefeatures, the electronic processor is configured to: analyze thedendritic structure to generate a representation of the dendriticstructure comprising a plurality of linear segments; and identify theone or more features from the representation of the dendritic structure.117. The system of claim 105, wherein prior to obtaining the at leastone image of the dendritic structure, the electronic processor isconfigured to select an information density level at which the dendriticstructure will be analyzed by selecting values associated with one ormore of a plurality of analysis attributes, and wherein the electronicprocessor is configured to select values associated with one or more ofthe plurality of analysis attributes by retrieving stored values of theone or more attributes based on information about an application of thedetermination of the numerical value.
 118. The system of claim 117,wherein the plurality of analysis attributes comprises at least one of anumber of readable states, a number of parameters used, a magnificationlevel, a fractal dimension of the dendritic structure, and a number ofimage pixels or grid locations used to analyze the dendritic structure.119. The system of claim 117, wherein the electronic processor isconfigured to: select a first information density level and analyze thedendritic structure at the first information density level; select asecond information density level and analyze the dendritic structure atthe second information density level using information derived from theanalysis of the dendritic structure at the first information densitylevel; and adjust the values associated with the one or more analysisattributes to select the second information density level.
 120. Amethod, comprising: obtaining at least one image of a dendriticstructure; analyzing the at least one image to identify one or morefeatures associated with the dendritic structure; and determining anumerical value associated with the dendritic structure based on the oneor more features.
 121. The method of claim 120, wherein the one or morefeatures comprise at least one of: one or more angles between segmentsof the dendritic structure; one or more lengths of segments of thedendritic structure; one or more distances of locations on the dendriticstructure from a reference point; and one or more angles of rotation oflocations on the dendritic structure relative to a reference line. 122.The method of claim 120, wherein determining the numerical valuecomprises determining a base n digit associated with each of at leastsome of the one or more features, wherein n is greater than
 2. 123. Themethod of claim 121, wherein at least one of: the one or more featurescomprises multiple angles between segments of the dendritic structureand the analyzing comprises comparing values of at least two of themultiple angles to determine the numerical value; and the one or morefeatures comprises multiple lengths of segments of the dendriticstructure and the analyzing comprises comparing values of at least twoof the multiple lengths to determine the numerical value.
 124. Themethod of claim 120, wherein the one or more features comprise a set ofcoordinates associated with a spatial distribution of the dendriticstructure on a coordinate system, the method further comprisingidentifying the set of coordinates by determining portions of thecoordinate system into which the dendritic structure extends by morethan a threshold amount.